Question

13. Find the measure of an angle if its measure is eight less than six times its complement.

Answer 1

For an instance, the measure of the angle is represented by y, and the measure of its complement is represented by x. We should write the expression for the problem.
⇒ We can express "eight less" as -8
⇒ We can express "six times its complement" as 6x
The first equation will be
y = 6x - 8

In the second equation, we will describe about the complementary angles. If they add up, the result is 90°. The second equation will be
x + y = 90

Using substitution method, we will find the value of x
x + y = 90
x + 6x - 8 = 90
7x - 8 = 90
7x = 90 - 8
7x = 82
  x = 82/7

Using substitution method, we find the value of y
y = 6x - 8
y = 6(82/7) - 8
y = 492/7 - 8
y = $\frac{492}{7}- \frac{56}{7}$
y = $\frac{436}{7}$
y = 62.3
to the near whole number
y = 62

The measurement of the angle is 62°