Chapter 2.2, Problem 13PSB

a)

To determine

Fill in the blanks with explanation in statements (a)

Answer to Problem 13PSB

Each is equal to ${90}^{\circ }$

Explanation of Solution

Given information: Two angles are congruent and supplementary

Let measure of each angles be $x^{\circ }$ .

Since these are supplementary hence their sum is ${180}^{\circ }$

  $\begin{array}{l}\therefore x^{\circ }+x^{\circ }={180}^{\circ }\\ \therefore x={90}^{\circ }\end{array}$

b)

To determine

Fill in the blanks with explanation in statements (2)

Answer to Problem 13PSB

Each is equal to ${45}^{\circ }$

Explanation of Solution

Given information: Two angles are congruent and complementary

let measure of each angles be $y^{\circ }$ .

Since these are supplementary hence their sum is ${90}^{\circ }$

  $\begin{array}{l}\therefore y^{\circ }+y^{\circ }={90}^{\circ }\\ \therefore y={45}^{\circ }\end{array}$