SUPPLEMENTARY ANGLES

About "Supplementary angles"

"Supplementary angles"  is the much required stuff for the students who stuff math in school level. 

Let us have a clear understanding about supplementary-angles. 

Supplementary-Angles  :

If the sum of two angles is 180⁰, then those two angles are called as supplementary-angles.

Example :

Example, 120° and 60° are supplementary-angles.

Because 120° + 60° = 180°.

Clearly, 120° is the supplement  of 60° and 60° is the supplement of 120°.

Let us see, how the stuff "supplementary angles" appears on picture.

Example problems

Example 1 :

The measure of an angle is 108°. What is the measure of a supplementary angle?

Solution :

Let "x" be the measure of a supplementary-angle required.

Since "x" and 108° are supplementary-angles, we have

x + 108° = 180°

x = 180° - 108°

x = 72°

Hence the measure of the supplementary-angle is 72°

Example 2 :

The measure of an angle is 89°. What is the measure of a supplementary-angle?

Solution :

Let "x" be the measure of a supplementary-angle required.

Since "x" and 41° are supplementary-angles, we have

x + 89° = 180°

x = 180° - 89°

x = 91°

Hence the measure of the supplementary-angle is 91°

Example 3 :

Two angles are supplementary. 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)

From the information, "one angle is two times the sum of other angle and 3", we have

x = 2(y+3)

x = 2y + 6 ------->(2)

Now plug x = 2y + 6 in equation (2)

(1)-------> 2y + 6 + y  = 90

3y + 6 = 90

3y = 84

y = 28

Now, plug y = 28 in equation (2).

(2) --------> x = 2(28) + 6

x = 56 + 6

x = 62

Hence the two angles are 62° and 28°

Example 4 :

Two angles are supplementary. If one angle is 36° less than twice of the other angle, find the two angles. 

Solution :

Let "x" and "y" be the two angles which are supplementary.

So, we have  x + y = 180° ----------->(1)

From the information, "one angle is 36

From the information, "one angle is 36° less than twice of the other angle", we have 

x = 2y - 36 ----------->(2)

Now plug x = 2y - 36 in equation (1)

(1)-------> 2y - 36 + y  = 180

3y - 36 = 180

3y = 216

y = 72

Now, plug y = 72 in equation (2).

(2) --------> x = 2(72) - 36

x = 144 - 36

x = 108

Hence the two angles are 108° and 72°

Example 5 :

Two angles are supplementary. If 5 times of one angle is 10 times of the other angle. Find the two angles.

Solution :

Let "x" and "y" be the two angles which are supplementary.

So, we have x + y = 180° -------->(1)

From the information, "5 times of one angle is 10 times of the other angle", we have

5x = 10y  =====> x = 2y ---------(2)

Plug x = 2y in equation (1)

2y + y = 180

3y = 180

y = 60

Plug y = 60 in equation (2)

x = 2(60)

x = 120

Hence the two angles are 60° and 120°.

Example 6 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that (2x+3) and (x-6) are supplementary-angles. 

So, we have (2x+3) + (x-6)  = 180°

3x - 3 = 180°

3x  = 183

x = 61

Hence the value of "x" is 61

Example 7 :

Find the value of  "x" in the figure given below.

Solution :

From the picture above, it is very clear that (5x+4), (x-2) and (3x+7) are supplementary-angles. 

So, we have (5x+4) + (x-2) + (3x+7) = 180°

5x + 4 + x -2 + 3x + 7 = 180°

9x + 9 = 180

9x = 171

x = 19

Hence the value of "x" is 19

After having gone through the stuff and problems on supplementary-angles,  we hope that the students would have understood "How to do problems on supplementary angles".

Do you want to know about complementary angles?

Please click here

To know more about problems on complementary and supplementary angles, please click here