Question

if an angle is 60° more than half of its complement, find its measure

Answer 1

(90-x)/2+60=x
=>(90-x)/2=x-60
=> (90-x)= 2(x-60)
=> 90-x=2x-120
=>210=3x
=>x=70°

Answer 2

Given: An angle is 60° more than half of its complement.

To find: The measure of the angle.

Solution:

The complement of an angle is the difference between 90° and the angle. The half of a compliment angle is the complement angle divided by 2. Since the angle is 60° more, 60° must be added to half of the angle's complement.

Let the angle be equal to x. Now, the equation to find the angle is written as follows.

$x = \frac{90 - x}{2} + 60$

$2x = 90 - x +120$

$3x = 210$

$x = 70$

Therefore, the measure of the angle is 70.