"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, 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 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° **

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° **

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****°.**

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? **

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

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