Question

The system of equations below represents the measures of 2 angles created by the diagonal of a rectangle:

x + y = 90

y = x/5

What is the measure of the greater angle?

15759045°

What is the measure of the smaller angle?

Answer 1

let
x-------> the greater angle
y-------> the smaller angle

we know that
x+y=90------> equation 1
y=x/5-------> equation 2

substitute equation 2 in equation 1
x+[x/5]=90-----> multiply by 5 both sides------> 5x+x=450
6x=450
x=75
y=x/5-----> y=75/5-----> y=15

the answer Part a) is
the greater angle is 75°

the answer part b) is
the smaller angle is 15°