Respuesta :
The measure of one angle is 76 degrees and other angle is 14 degrees
Solution:
Given that two angles are complementary
Let "a" be the one of complementary angle and "b" be the other complementary angle
Two angles are Complementary when they add up to 90 degrees
a + b = 90 ----- eqn 1
Given that the measure of one angle is 6 more than five times the measure of the other angle.
measure of one angle = 6 + 5(measure of the other angle)
a = 6 + 5(b)
a = 6 + 5b ----- eqn 2
Let us solve eqn 1 and eqn 2 to find "a" and "b"
from eqn 1,
b = 90 - a ------- eqn 3
Substitute eqn 3 in eqn 2
a = 6 + 5(90 - a)
a = 6 + 450 - 5a
6a = 456
a = 76
Therefore from eqn 3,
b = 90 - a = 90 - 76 = 14
b = 14
Thus measure of one angle is 76 degrees and other angle is 14 degrees
