Answer:
The measurement of x is 106° and the measurement of y is 74°.
Step-by-step explanation:
The definition of an isosceles trapezoid is a trapezoid that has two pairs of congruent base angles. One pair at the top and the other pair at the bottom.
When you look at the trapezoid, you are given an angle. This angle measures 74°. Since base angles are congruent in an isosceles trapezoid, then the measurement of y is also 74°.
Another thing about isosceles trapezoids and all trapezoids is that they all have an interior angles sum of 360°. Interior means all of the angles inside the shape. So, since we know the bottom base angles both have a measurement of 74°, then we can add these angles together.
74 + 74 = 148
Now, we subtract 148 from 360 so we can find the measurement of x.
360 - 148 = 212
Now since there are two top base angles, then we will divide 2 from 212.
212 ÷ 2 = 106
So, the measurement of x is 106°.
