Question

The isosceles trapezoid is part of an isosceles triangle with a 32° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale.

Answer 1

Answer:

acute base angle = 74° , obtuse base angle = 106°

Step-by-step explanation:

Since the large triangle is isosceles with vertex angle (top angle) is 32, then the bottom 2 angles would be same (let it be x):

We know angles of triangle add up to 180, so we have:

x + x + 32 = 180

2x = 180 - 32

2x = 148

x = 148/2

x = 74

This 74 degree angle is the base acute angle of the isosceles trapezoid (lower portion). We also know opposite angles of isosceles trapezoid are supplementary (add up to 180), thus

obtuse angle + 74 = 180

obtuse angle (base) = 180 - 74 = 106

Thus, acute base angle = 74° , obtuse base angle = 106°