Lines and Angles Test - 4

Two Angles are complementary when they add up to 90 degrees (a Right Angle).

Option A:

52° + 38° = 90°

So, these are complementary angles.

Option B:

115° + 21° = 136°

These are not complementary angles.

Option C:

77° + 14° = 91°

These are not complementary angles.

Option D:

155° + 23° = 178°

These are not complementary angles.

Hence, option A is correct.

When two angles are supplementary, each angle is said to be the supplement of the other.

So, let the supplement angle be x.

As we know that the sum of measurement of supplementary angles is 180°.

⇒ 105° + x = 180°

⇒ x = 180° - 105°

⇒ x = 75°

So, 75° is the supplement of 105° as 105° + 75° = 180°.

Hence, option D is correct.

As we know,

The sum of measure of angles of a linear pair is 180°.

So, if one of the angles is obtuse, the other must be acute.

Example:

If one angle is 105°.

The other will be 180° - 105° = 75° which is an acute angle.

Hence, option A is correct.

Two Angles are complementary when they add up to 90° (a Right Angle).

Hence, option C is correct.

Whenever two angles are complementary, each angle is said to be the complement of the other angle.

So, let the complement angle be x.

As we know sum of the measure of complementary angles is 90°.

⇒ 50° + x = 90°

⇒ x = 90° - 50°

⇒ x = 40°

So, 40° is complement of 50° as 50° + 40° = 90°.

Hence, option C is correct.

We know two Angles are supplementary when they add up to 180 degrees.

Here, 100° + 80° = 180°

So, the sum of the measure of angles 100° and 80° makes supplementary angles.

Hence, option D is correct.

When two angles are supplementary, each angle is said to be the supplement of the other.

So, let the supplement angle be x.

As we know that the sum of measurement of supplementary angles is 180°.

⇒ 155° + x = 180°

⇒ x = 180° - 155°

⇒ x = 25°

So, 25° is the supplement of 155° as 155° + 25° = 180°.

Hence, option B is correct.