How to find an angle in an acute / obtuse triangle

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

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

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.