Question

in the figure below, m∠1=(x + 42)° and m∠2 = 2x°. find the angle measures. m∠1 = □° m∠2 = □°

Explanation:

Step1: Note angle - sum property

Since ∠1 and ∠2 are complementary, m∠1 + m∠2=90°.

Step2: Substitute angle expressions

(x + 42)+2x = 90.

Step3: Combine like - terms

3x+42 = 90.

Step4: Solve for x

3x=90 - 42, 3x = 48, x = 16.

Step5: Find m∠1 and m∠2

m∠1=x + 42=16 + 42 = 58°. m∠2=2x=2×16 = 32°.

Answer:

m∠1 = 58°, m∠2 = 32°