Question

1. ∠a and ∠b are complementary angles. if the measure of ∠a is 42°, find the measure of ∠b. 9. ∠1 and ∠2 form a linear pair. if the measure of ∠1 is 113°, find the measure of ∠2.

Explanation:

Problem 7: Complementary Angles

Step1: Recall complementary angles sum to 90°.

Let \( m\angle A = 42^\circ \), \( m\angle B = x \). Then \( 42^\circ + x = 90^\circ \).

Step2: Solve for \( x \).

\( x = 90^\circ - 42^\circ = 48^\circ \).

Step1: Recall linear pair angles sum to 180°.

Let \( m\angle 1 = 113^\circ \), \( m\angle 2 = y \). Then \( 113^\circ + y = 180^\circ \).

Step2: Solve for \( y \).

\( y = 180^\circ - 113^\circ = 67^\circ \).

Answer:

The measure of \( \angle B \) is \( 48^\circ \).

Problem 9: Linear Pair Angles