Question

If angle A is 5 times its complimentary angle and 5/7 of its supplementary angle,then measure of angle A is how much?

Answer 1

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Step-by-step explanation:Two angles are called complementary angles, if their sum is one right angle i.e. 90°.

Each angle is called the complement of the other.

Example, 20° and 70° are complementary angles, because 20° + 70° = 90°.

Clearly, 20° is the complement of 70° and 70° is the complement of 20°.

Thus, the complement of angle 53° = 90° - 53° = 37°.

Supplementary Angles:

Two angles are called supplementary angles, if their sum is two right angles i.e. 180°.

Each angle is called the supplement of the other.

Example, 30° and 150° are supplementary angles, because 30° + 150° = 180°.

Clearly, 30° is the supplement of 150° and 150° is the supplement of 30°.

Thus, the supplement of angle 105° = 180° - 105° = 75°.

Solved problems on complementary and supplementary angles:

1. Find the complement of the angle 2/3 of 90°.

Solution:

Convert 2/3 of 90°

2/3 × 90° = 60°

Complement of 60° = 90° - 60° = 30°

Therefore, complement of the angle 2/3 of 90° = 30°

2. Find the supplement of the angle 4/5 of 90°.

Solution:

Convert 4/5 of 90°

4/5 × 90° = 72°

Supplement of 72° = 180° - 72° = 108°

Therefore, supplement of the angle 4/5 of 90° = 108°

3. The measure of two complementary angles are (2x - 7)° and (x + 4)°. Find the value of x.

Solution:

According to the problem, (2x - 7)° and (x + 4)°, are complementary angles’ so we get;

(2x - 7)° + (x + 4)° = 90°

or, 2x - 7° + x + 4° = 90°

or, 2x + x - 7° + 4° = 90°

or, 3x - 3° = 90°

or, 3x - 3° + 3° = 90° + 3°

or, 3x = 93°

or, x = 93°/3°

or, x = 31°

Therefore, the value of x = 31°.

4. The measure of two supplementary angles are (3x + 15)° and (2x + 5)°. Find the value of x.

Solution:

According to the problem, (3x + 15)° and (2x + 5)°, are complementary angles’ so we get;

(3x + 15)° + (2x + 5)° = 180°

or, 3x + 15° + 2x + 5° = 180°

or, 3x + 2x + 15° + 5° = 180°

or, 5x + 20° = 180°

or, 5x + 20° - 20° = 180° - 20°

or, 5x = 160°

or, x = 160°/5°

or, x = 32°

Therefore, the value of x = 32°.

5. The difference between the two complementary angles is 180°. Find the measure of the angle.

Solution:

Let one angle be of measure x°.

Then complement of x° = (90 - x)

Difference = 18°

Therefore, (90° - x) – x = 18°

or, 90° - 2x = 18°

or, 90° - 90° - 2x = 18° - 90°

or, -2x = -72°

or, x = 72°/2°

or, x = 36°

Also, 90° - x

= 90° - 36°

= 54°.

Therefore, the two angles are 36°, 54