How to find an angle in a hexagon

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PSAT Math › How to find an angle in a hexagon

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Hexagon

Note:Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

CORRECT

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

Hexagon

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

CORRECT

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

We can solve for in the equation

Three angles of a hexagon measure $65^{\circ}, 74^{\circ}, 89^{\circ}$ . The other three angles are congruent to one another. What is the measure of each of the latter three angles?

$164^{\circ}$

CORRECT

This hexagon cannot exist.

$174^{\circ}$

$48^{\circ}$

$58^{\circ}$

Explanation

The sum of the degree measures of the angles of a (six-sided) hexagon, is

$180 ^{\circ } \times (6 - 2) = 180 ^{\circ } \times 4 = 720^{\circ }$

Let be the common measure of the three congruent angles in question. We can solve for in the equation

In a rectangular hexagon, what is the meaure of each interior angle?

120 degrees

CORRECT

90 degrees

105 degrees

150 degrees

72 degrees

Explanation

The sum of the interior angles of a hexagon must equal 720 degrees. Because the hexagon is regular, all of the interior angles will have the same measure. A hexagon has six sides and six interior angles. Therefore, each angle measures $\frac{720}{6}=120$ .

What is the measurement of one of the interior angles of a regular hexagon?

$120^\circ$

CORRECT

$90^\circ$

$150^\circ$

$135^\circ$

$105^\circ$

Explanation

To find the sum of the interior angles of any regular polygon, use the formula $(n-2)\cdot180$ , where represents the number of sides of the regular polygon.

$=(6-2)\cdot180$

$=4\cdot180$

The sum of the interior angles of a regular hexagon is 720 degrees. To find the measurement of one angle, divide by the number of interior angles (or sides):