Question

The difference in the measures of two complementary angles is 12 degree. Find the measures of the angles

Answer 1

Let one angle be x
Then,
Its complementary angle will be =(90-x)

ATQ,
x-(90-x)=12
x-90+x=12
x+x=12+90
2x=102
x=102/2
x=51

Thus,
x=51
(90-x)=(90-51)=39

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Answer 2

Given:

The difference in the value of two complementary angles is 12 degrees.

To find:

To calculate the measure of the two complementary angles.

Solution:

Complementary angles are those angles whose sum is equal to 90 degrees.

Therefore, if two angles are called complementary, then the sum of the measure of the two angles must be equal to 90 degrees.

Let us take one angle as Y degree and the other as (90-Y) degree.

Since the difference is equal to 12 degrees,

This implies that,

Y – ( 90 – Y ) = 12

Y- 90 +Y = 12

2Y – 90 = 12

2Y = 90 + 12

2Y = 102

Y = 51

One of the two angles is equal to 51.

Other angle = 90-Y = 90 – 51

= 39

The measure of the two complementary angles is 51 degrees and 39 degrees.