Question

The difference in the measures of two complementary angles is 12°. Find the smallest angle.

Answer 1

Answer:

Complementary Angles:

Definition: A pair of angles which sums up to 90° are called complementary angles and one angle is said to be a complement of the other.

Uses: Used for finding properties of various polygons.

Example: 30°, 60° [30+60 = 90°].

Method 1:

So, coming to the question, we have been given the difference between 2 complementary angles and are supposed to find their sum.

Let the larger angle be denoted by the variable x and the smaller angle be denoted by the variable y.

Now, we have to form 2 linear equations in 2 variables.

Equation 1:

x + y = 90.

Equation 2:

x - y = 12.

Adding equation 1 and equation 2:

(x + y) + (x - y) = 90+12.

2x = 102.

x = 102/2

x = 51°.

Substituting the value of x in equation 2:

(51) - y = 12

- y = 12-51

- y = - 39

y = 39°.

Method 2:

This can also be solved using linear equation in 1 variable where x is the larger angle and the smaller angle is x-12.

We know that their sum is 90°.

(x) + (x - 12) = 90.

2x = 102.

x = 51°

x - 12 = 51 - 12 = 39°

Therefore, the 2 complementary angles are 51° and 39°.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

let bigger angle=x

then smaller angle=x-12°

so

x+x-12°=90°

2x=102°

x=51°

x-12°=51°-12°=39°