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

1 Answer
Jan 2, 2016

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.

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