Question

Which of the following is true?

• A. Angles forming a linear pair can both be acute angles.
• B. If two lines are intersected by a transversal, then corresponding angles are equal.
• C. The supplementary angles have their sum equal to $360°$.
• D. Two angles are complementary if their sum is $90°$.

Answer 1

The correct option is D

Two angles are complementary if their sum is $90°$.

Explanation for the correct option:

Option (D): Two angles are complementary if their sum is $90°$.

It is known that two angles are said to be complementary when their measures add to $90°$.

Therefore, the statement " Two angles are complementary if their sum is $90°$." is true.

Explanation for the incorrect options:

Option (A): Angles forming a linear pair can both be acute angles.

It is known that the sum of the measures of two acute angles is always less than $180°$ degrees,

Thus, two acute angles can never form a linear pair.

Therefore, the statement “Angles forming a linear pair can both be acute angles.” is false.

Option (B): If two lines are intersected by a transversal, then corresponding angles are equal.

It is known that when two lines are intersected by a transversal, the corresponding angles may not be equal.
Such angles would be equal only in the case of parallel lines.

Therefore, the statement "If two lines are intersected by a transversal, then corresponding angles are equal." is false.

Option (C): The supplementary angles have their sum equal to $360°$.

It is known that the supplementary angles have their sum equal to $180°$.

Therefore, the statement " The supplementary angles have their sum equal to $360°$." is false.

Hence, option (D) is correct.