# COMPLEMENTARY ANGLES

Complementary Angles :

Two angles are complementary, if they add up to 90⁰.

Example :

30° and 60° are complementary angles.

Because,

30° + 60°  =  90°

Clearly, 30° is the complement of 60° and 60° is the complement of 30°. ## Complementary Angles - Practice Problems

Problem 1 :

The measure of an angle is 41°. What is the measure of a complementary angle?

Solution :

Let x be the measure of the required complementary angle.

Because x and 41° are complementary angles,

x + 41°  =  90°

Subtract 41° from each side.

x = 49°

So, the measure of the complementary angle is 49°.

Problem 2 :

The measure of an angle is 62°. What is the measure of a complementary angle?

Solution :

Let x be the measure of the required complementary angle.

Because x and 62° are complementary angles,

x + 62°  =  90°

Subtract 62° from each side.

x  =  28°

So, the measure of the complementary angle is 28°.

Problem 3 :

Find the value of  x : Solution :

From the picture above, it is clear that the angles x and 2x are complementary.

Then,

x + 2x  =  90

Simplify.

3x  =  90

Divide each side by 3.

x  =  30

So, the value of x is 30.

Problem 4 :

Find the value of  x : Solution :

From the picture above, it is clear that the angles (x+1), (x-1) and (x+3) are complementary.

Then,

(x+1) + (x-1) + (x+3)  =  90

x + 1 + x - 1 + x + 3  =  90

Simplify.

3x + 3  =  90

Subtract 3 from each side.

3x  =  87

Divide each side by 3.

x  =  29

So, the value of x is 29.

Problem 5 :

Two angles are complementary. If one of the angles is double the other angle, find the two angles.

Solution :

Let x be one of the angles.

Then the other angle is 2x.

Because x and 2x are complementary angles, we have

x + 2x  =  90°

3x  =  90

Divide each side by 3.

x  =  30

And,

2x  =  2(30)  =  60

So, the two angles are 30° and 60°.

Problem 6 :

Two angles are complementary. If one angle is two times the sum of other angle and 3, find the two angles.

Solution :

Let x and y be the two angles which are complementary.

So, we have

x + y  =  90° -----> (1)

Given : One angle is two times the sum of other angle and 3.

Then,

x  =  2(y + 3)

x  =  2y + 6 ----->(2)

Now, substitute (2y + 6) for x in (1).

(1)-----> 2y + 6 + y  =  90

3y + 6  =  90

Subtract 6 from each side.

3y  =  84

Divide each side by 3.

y  =  28

Substitute 28 for y in (2).

(2)-----> x  =  2(28) + 6

x  =  56 + 6

x  =  62

So, the two angles are 62° and 28°. After having gone through the stuff given above, we hope that the students would have understood supplementary angles.

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