Question

The system of equations below represents the measures of 2 angles created by the diagonal of a rectangle: x + y = 90 y = y equals StartFraction x over 5. What is the measure of the greater angle? ° What is the measure of the smaller angle? °

Answer 1

Answer:

Greater angle=75° Smaller angle=15°

Step-by-step explanation:

Given expressions

• x+y=90
• y=$\frac{x}{5}$

⇒$y=\frac{x}{5}\\ x=5\times y$

Substitute this in the first expression

⇒ x+y=90

$5\times y+ y=90\\6\times y =90\\y=\frac{90}{6} \\y=15$

From the First expression

Substitute y value to get x value

⇒$x+y=90\\x+15=90\\x=75$

Therefore x=75 and y=15

⇒ Greater angle=75 and smaller angle=15