Two complementary angles differ by 12 degrees, find the angles.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Two complementary angles differ by 12 degrees, the angles are 390, and 510. Now we have to find the angles:

Let one of the angles be x

Differences between the two complementary angles are 120

Therefore, the bigger angle = (x + 12)

We know that Sum of Complementary angles = 900

x + x + 120 = 900

2x + 120 = 900

On rearranging we get:

2x = (90 – 12)0

2x = 78

In simplification we get the:

x = 78/2

x = 390

The smaller angle will be 390

Bigger angle (x + 12) = 39 + 12 = 510

Therefore the angles are 390, and 510 degrees respectively.

Table of content

1. Two complementary angles differ by 12 degrees, find the angles.

Complementary Angles

Two angles are said to be complimentary if they combine to make a right angle.
In this case, we say that the two angles work well together.

How can one determine complementary angles?

Consider the case where one angle is x and the other is 90° – x. Thus, for trigonometric ratios when one ratio is complementary to another ratio by 90 degrees, such as; we employ these complementary angles.

tan (90° – A) = cot A and cot (90° – A) = tan A
sin (90° – A) = cos A and cos (90° – A) = sin A
sec (90° – A) = cosec A and cosec (90° – A) = sec A

Summary: