Triangles - GRE Quantitative Reasoning
Card 1 of 552
A triangle has three internal angles of 75, 60, and x. What is x?
A triangle has three internal angles of 75, 60, and x. What is x?
Tap to reveal answer
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
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A triangle has three internal angles of 75, 60, and x. What is x?
A triangle has three internal angles of 75, 60, and x. What is x?
Tap to reveal answer
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
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A triangle has three internal angles of 75, 60, and x. What is x?
A triangle has three internal angles of 75, 60, and x. What is x?
Tap to reveal answer
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
The internal angles of a triangle must add up to 180. 180 - 75 -60= 45.
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An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
Tap to reveal answer
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
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An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
Tap to reveal answer
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
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Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Tap to reveal answer
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
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An isosceles triangle has one obtuse angle that is 
. What is the value of one of the other angles?
An isosceles triangle has one obtuse angle that is
Tap to reveal answer
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
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An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
Tap to reveal answer
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
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An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
Tap to reveal answer
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
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Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Tap to reveal answer
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
← Didn't Know|Knew It →
An isosceles triangle has one obtuse angle that is . What is the value of one of the other angles?
An isosceles triangle has one obtuse angle that is
Tap to reveal answer
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
← Didn't Know|Knew It →
An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
An isosceles triangle has an angle of 110°. Which of the following angles could also be in the triangle?
Tap to reveal answer
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
An isosceles triangle always has two equal angles. As there cannot be another 110° (the triangle cannot have over 180° total), the other two angles must equal eachother. 180° - 110° = 70°. 70° represents the other two angles, so it needs to be divided in 2 to get the answer of 35°.
← Didn't Know|Knew It →
An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
An isosceles triangle ABC is laid flat on its base. Given that <B, located in the lower left corner, is 84 degrees, what is the measurement of the top angle, <A?
Tap to reveal answer
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
Since the triangle is isosceles, and <A is located at the top of the triangle that is on its base, <B and <C are equivalent. Since <B is 84 degrees, <C is also. There are 180 degrees in a triangle so 180 - 84 - 84 = 12 degrees.
← Didn't Know|Knew It →
Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Triangle ABC is isosceles
x and y are positive integers
A
---
x
B
---
y
Tap to reveal answer
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
Since we are given expressions for the two congruent angles of the isosceles triangle, we can set the expressions equal to see how x relates to y. We get,
x – 3 = y – 7 --> y = x + 4
Logically, y must be the greater number if it takes x an additional 4 units to reach its value (knowing they are both positive integers).
← Didn't Know|Knew It →
An isosceles triangle has one obtuse angle that is . What is the value of one of the other angles?
An isosceles triangle has one obtuse angle that is
Tap to reveal answer
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.
180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.
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In the figure above, what is the value of angle x?
In the figure above, what is the value of angle x?
Tap to reveal answer
To find the top inner angle, recognize that a straight line contains 180o; thus we can subtract 180 – 115 = 65o. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95o.
180 - 95 = 85
To find the top inner angle, recognize that a straight line contains 180o; thus we can subtract 180 – 115 = 65o. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95o.
180 - 95 = 85
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The three angles in a triangle measure 3_x_, 4_x_ + 10, and 8_x_ + 20. What is x?
The three angles in a triangle measure 3_x_, 4_x_ + 10, and 8_x_ + 20. What is x?
Tap to reveal answer
We know the angles in a triangle must add up to 180, so we can solve for x.
3_x_ + 4_x_ + 10 + 8_x_ + 20 = 180
15_x_ + 30 = 180
15_x_ = 150
x = 10
We know the angles in a triangle must add up to 180, so we can solve for x.
3_x_ + 4_x_ + 10 + 8_x_ + 20 = 180
15_x_ + 30 = 180
15_x_ = 150
x = 10
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In triangle ABC, AB=6, AC=3, and BC=4.
Quantity A Quantity B
angle C the sum of angle A and angle B
In triangle ABC, AB=6, AC=3, and BC=4.
Quantity A Quantity B
angle C the sum of angle A and angle B
Tap to reveal answer
The given triangle is obtuse. Thus, angle 
is greater than 90 degrees. A triangle has a sum of 180 degrees, so angle 
+ angle 
+ angle 
= 180. Since angle C is greater than 90 then angle 
+ angle 
must be less than 90 and it follows that Quantity A is greater.
The given triangle is obtuse. Thus, angle
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In the figure above, what is the value of angle x?
In the figure above, what is the value of angle x?
Tap to reveal answer
To find the top inner angle, recognize that a straight line contains 180o; thus we can subtract 180 – 115 = 65o. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95o.
180 - 95 = 85
To find the top inner angle, recognize that a straight line contains 180o; thus we can subtract 180 – 115 = 65o. Since we are given the other interior angle of 30 degrees, we can add the two we know: 65 + 30 = 95o.
180 - 95 = 85
← Didn't Know|Knew It →
The three angles in a triangle measure 3_x_, 4_x_ + 10, and 8_x_ + 20. What is x?
The three angles in a triangle measure 3_x_, 4_x_ + 10, and 8_x_ + 20. What is x?
Tap to reveal answer
We know the angles in a triangle must add up to 180, so we can solve for x.
3_x_ + 4_x_ + 10 + 8_x_ + 20 = 180
15_x_ + 30 = 180
15_x_ = 150
x = 10
We know the angles in a triangle must add up to 180, so we can solve for x.
3_x_ + 4_x_ + 10 + 8_x_ + 20 = 180
15_x_ + 30 = 180
15_x_ = 150
x = 10
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