Question

Which two statements contradict each other?

I. ∠1 and ∠2 are complementary angles.
II. m∠1 = 65°
III. m∠1 + m∠2 + m∠3 = 90°; m∠3 ≠ 0
A. No two statements contradict each other.
B. I and II
C. I and III
D. II and III

Answer 1

The two statements that contradict each other are I. ∠1 and ∠2 are complementary angles and II. m∠1 = 65°.

Step-by-step explanation:

The statements in question are I. ∠1 and ∠2 are complementary angles and II. m∠1 = 65°.

∠1 and ∠2 are said to be complementary angles when the sum of their measures equals 90°. Therefore, statement I implies that ∠1 + ∠2 = 90°.

However, statement II states that m∠1 = 65°, which contradicts the previous statement since m∠1 + m∠2 ≠ 90°.

Therefore, the two contradicting statements are I and II.