Supplementary Angles Formula

Before going to learn what is supplementary angles formula, first, let us recall what are supplementary angles. Two angles are said to be supplementary if their sum is 180° and in this case, one angle is said to be the supplement of the other. We use this fact to derive the supplementary angles formula. 

What Is Supplementary Angles Formula?

We come across the concept of supplementary angles while solving many problems related to different shapes. The supplementary angles formula is used to:

• determine whether two angles are supplementary.
• find the supplement of an angle.

Two angles x° and y° are said to be supplementary if

x° + y° = 180°

The supplement of an angle x° is obtained by subtracting it from 180°.

Supplement of x° = (180 - x)°

Let us see the applications of the supplementary angles formulas in the following section.

Examples on Supplementary Angles Formula

Example 1: Determine whether the following pairs of angles are supplementary using the supplementary angles formulas. (a) 50° and 130°  (b) 70° and 100°

Solution:

To find: Whether the given pairs of angles are supplementary.

We know that two angles are supplementary if their sum is 180°.

(a) 50° + 130° = 180°

Since the sum is 180°, the given angles are supplementary.

(b) 70° + 100° = 170°

Since the sum is NOT 180°, the given angles are NOT supplementary.

Answer: (a) Supplementary; (b) NOT supplementary.

Example 2: If two angles (3x + 15)° and (5x + 80)° are supplementary, then find the value of x.

Solution:

To find: The value of x.

Since the angles (3x + 15)° and (5x + 80)° are supplementary, using the supplementary angles formula, their sum is 180°.

(3x + 15) + (5x + 80) = 180

8x + 95 = 180

Subtracting 95 from both sides,

8x = 85

Dividing both sides by 8,

x = 85/8

Answer: x = 85/8