please answer the question

Question

Use the figure shown.

What is m∠2?

1. A=45

1. B.=18

1. C.=12

1. D.=120

Answer 1

Hi Shireen,

The two vertical lines in this problem are parallel, as indicated in the diagram. If you turn your head sideways, you'll see that there is an F pattern (corresponding angles), so that means that:

(5x) + (3x + 9) = (9x - 3)

(I used parentheses above just so that you can see which angles I'm referring to.)

I'll rewrite it as:

5x + 3x + 9 = 9x - 3

If we go ahead and solve this for x, we get:

8x + 9 = 9x - 3

12 = x

Go ahead and substitute x = 12 in to the expression 3x + 9.

This will give you: 3(12) + 9 = 36 + 9

= 45 degrees

Since angle 2 and (3x+9) are vertical angles, they are congruent. That means that angle 2 also measures 45 degrees.

I hope this helps!