Question

7 part a (a) if ∠a and ∠b are supplementary angles, what angle relationship between ∠a and ∠b cannot be true? a ∠a and ∠b are right angles. b ∠a and ∠b are complementary angles. c ∠a and ∠b are adjacent angles. d ∠a and ∠b are congruent angles.

Explanation:

• For option A: If \(\angle A = 90^{\circ}\) and \(\angle B=90^{\circ}\), then \(\angle A+\angle B = 90^{\circ}+90^{\circ}=180^{\circ}\). So, supplementary angles can both be right - angles.
• For option B: Complementary angles add up to \(90^{\circ}\). Supplementary angles add up to \(180^{\circ}\). If \(\angle A+\angle B = 180^{\circ}\), they cannot also add up to \(90^{\circ}\).
• For option C: Adjacent angles can be supplementary. For example, two angles forming a linear pair (adjacent and supplementary) like \(\angle A\) and \(\angle B\) where one side is common and they form a straight line.
• For option D: If \(\angle A=\angle B\), then \(2\angle A = 180^{\circ}\) (since \(\angle A+\angle B = 180^{\circ}\)), so \(\angle A=\angle B = 90^{\circ}\). Congruent (equal - measure) angles can be supplementary.

Answer:

B. \(\angle A\) and \(\angle B\) are complementary angles.