Question

Think About the Process In the​ diagram, m∠1=(117−y)°​, m∠2=25°​, and m∠3=(x+46)°. Write an equation to solve for x and an equation to solve for y. Find the values of x and y.

1

2

3

​(The figure is not shown to​ scale.)

Write an equation to solve for x and an equation to solve for y. Choose the correct answer below.

A.

25+x+46=90 and 117−y=90

B.

x+46=90 and 25+117−y=90

C.

25+x+46=90 and 117−y=180

D.

25+x+46=180 and 117−y=90

Answer 1

A

Explanation:

∠1 is a right angle

Right angles have a measure of 90°

If ∠1 = 117 - y

Then 117 - y = 90

∠2 and ∠3 create a right angle

Like stated previously right angles have measures of 90°

This means that ∠2 + ∠3 = 90

So if ∠2 = 25 and ∠3 = x + 46

Then 25 + x + 46 = 90

The equations created correspond with the answer choice A

Therefore A is the correct answer