The measures of two complementary angles are 64 degrees and 26 degrees
Solution:
Let the larger angle be "a" and smaller angle be "b"
Two angles are Complementary when they add up to 90 degrees
so we get,
a + b = 90 ------ eqn 1
Given that measure of the larger angle is 12 more than twice the measure of the smaller angle
larger angle = 12 + 2(smaller angle)
a = 12 + 2b --- eqn 2
Let us solve eqn 1 and eqn 2 to get values of "a" and "b"
Substitute eqn 2 in eqn 1
12 + 2b + b = 90
12 + 3b = 90
3b = 90 - 12
3b = 78
b = 26
Therefore from eqn 2,
a = 12 + 2b
a = 12 + 2(26)
a = 12 + 52
a = 64
Thus the measures of two complementary angles are 64 degrees and 26 degrees