Question

Two angles are congruent and complementary. What is the measure of each angle?

Answer 1

`45˚`

Explanation:

Congruent angles have the same measurement (are the same size). If `angle1congangle2`, then

`mangle1=x`
`mangle2=x`

holds true.

Complementary angles have a sum of `90˚`. Thus, if `angle1` and `angle2` are complementary,

`mangle1+mangle2=90`

Substitute the equivalent forms of these angle measurements `(x,x)`.

`x+x=90`

Solve algebraically.

`2x=90`
`x=45`

Each angle is `45˚`.

Since complementary angles' sum is `90˚`, they form a right angle.