Question

(d) problem 21: (first taught in lesson 51) find x. after you enter your answer press go. x =

Explanation:

Step1: Identify the type of trapezoid

The trapezoid has a pair of parallel sides (indicated by the arrows) and the non - parallel sides are equal (marked with the same tick marks). So, it is an isosceles trapezoid.

Step2: Use the property of adjacent angles in an isosceles trapezoid

In an isosceles trapezoid, adjacent angles along the non - parallel sides are supplementary. That is, the sum of adjacent angles is \(180^{\circ}\).
If one angle is \(100^{\circ}\), then \(x + 100^{\circ}=180^{\circ}\)

Step3: Solve for \(x\)

Subtract \(100^{\circ}\) from both sides of the equation \(x + 100^{\circ}=180^{\circ}\)
\(x=180^{\circ}- 100^{\circ}\)

Answer:

\(x = 80\)