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

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Answer 1 · 2016-01-02T03:43:30

$45˚$

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.

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