Question

If x=47° find the measures of angles 1, 2, 3

Answer 1

2 = 47 degrees

1 = 133 degrees

3 = 133 degrees

2 is opposite of x, so the angles are equal. Angle 2 is 47 degrees

A straight line is 180 degrees. Subtract 47 from 180 to get 133. Therefore, Angle 1 is 133 degrees. Because Angle 3 is opposite of Angle 1, it has the same angle as Angle 1. So Angle 3 is 133 degrees.

Answer 2

Since angles x and 2 are vertical angles, they are congruent, Therefore, angle 2 is also 47°

We know that angles x and 1 are supplementary (add to 180) because they are adjacent angles along a straight line. We we can write the equation:
180=47+x
x=133 (subtract 47 from both sides)
So angle 1 is 133°

Then since angles 1 and 3 are also supplementary, angle 3 is also 133°

Hope this helps