Chapter 12, Problem 9CR

To determine

To Calculate: The measure of $\angle R$

Answer to Problem 9CR

The measure of $\angle R$ is ${91}^{\circ }$

Explanation of Solution

Given information:

SPQR is an isosceles trapezoid.

The measures of $\angle S$ and $\angle Q$ are as follows:

  $\angle S={\left(x+40\right)}^{\circ }$

  $\angle Q={\left(2x-7\right)}^{\circ }$

Formula used:

Here, we are using angle sum property.

Calculation:

Here, we know that

SPQR is an isosceles trapezoid

So, $\angle S=\angle P$

  $\angle Q=\angle R$

And, $\angle S+\angle Q={180}^{\circ }$

(angle sum property)

  $\angle P+\angle R={180}^{\circ }$

So, $\angle S+\angle Q=\angle P+\angle R$

  $x+{40}^{\circ }+2x-7={180}^{\circ }$

  $3x={147}^{\circ }$

  $x={49}^{\circ }$

So that, $\angle Q=\angle R$

Hence, $\angle R={\left(2x-7\right)}^{\circ }$

  $\angle R={\left(2\times 49-7\right)}^{\circ }$

  $\angle R={91}^{\circ }$

Conclusion: Hence, the measure of $\angle R$ is ${91}^{\circ }$