Question

the difference in the measures of the two complementary angles is 12 find the measure of the angles

Answer 1

Let us assume the angle to be 'a'.

The Complement of a is given by = 90 - a

The Difference Between Both The Angles That Is Given In The Question

= 12

Calculating The Difference:

=> (90 - a ) - a = 12

Opening the bracket:

=> 90 - a - a = 12

=> 90 - 2a = 12

Taking 90 to the other side of the equation we get:

=> - 2a = 12 - 90

=> - 2a = - 78

Taking - 2 to the other side of the equation we get:

=> a = - 78 / - 2

=> a = 39

(When we divide a negative number by a negative number the result we obtain will always be positive)

Therefore, we obtain the value of 'a' as 39.

Therefore, the first complimentary angle is 39° as we assumed the first complimentary angle as 'a'.

Calculating the value of the second complimentary angle:

= 90 - a

= 90 - 39

= 51°

Therefore, the value of the second complimentary angle is 51°.