∠A and ∠B are supplementary, and ∠A and ∠C are supplementary. Which conclusion is valid? Select one: A. ∠B and ∠C are supplement

Question

4 years ago

8

ary. B. ∠B and ∠C are acute. C. ∠B and ∠C are complementary. D. ∠B and ∠C are congruent.

1 answer:

zysi [14] · Answer 1 · 2021-11-15T20:51:43+03:00

Option D is the correct answer.

Answer:

D. ∠B and ∠C are congruent.

Step-by-step explanation:

Since, ∠A and ∠B are supplementary.

Therefore,

∠A + ∠B = 180°.....(1)

Since, ∠A and ∠C are supplementary.

Therefore,

∠A + ∠C = 180°.....(2)

From equations (1) & (2)

∠A + ∠B = ∠A + ∠C

=> ∠B = ∠C

Hence, ∠B and ∠C are congruent.