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.