Question

∠1 and ∠2 are complementary given. m∠1 = 36° given. ∠2 and ∠3 are a linear pair given. 36°+m∠2 = 90° definition of complementary angles. m∠2 = 54° subtraction property of equality. 54°+m∠3 = 180° substitution property of equality. m∠2 + m∠3 = 180° linear pairs theorem. what is most likely being shown by the proof? a. m∠1 + m∠3 = 90° b. m∠3 = 144° c. m∠1 + m∠3 = 180° d. m∠3 = 126°

Explanation:

Step1: Find the measure of ∠2

Given ∠1 and ∠2 are complementary and m∠1 = 36°. By the definition of complementary angles (sum of complementary angles is 90°), we have 36°+m∠2 = 90°. Using the subtraction property of equality, m∠2=90° - 36° = 54°.

Step2: Find the measure of ∠3

Given ∠2 and ∠3 are a linear - pair. By the linear - pairs theorem (sum of angles in a linear pair is 180°), m∠2 + m∠3 = 180°. Substituting m∠2 = 54° into the equation, we get 54°+m∠3 = 180°. Using the subtraction property of equality, m∠3=180° - 54° = 126°.

Answer:

D. m∠3 = 126°