Question

Inscribed angles.
What is the value of x?

Answer 1

Notice the second drawing. The measure of an inscribed angle is half the measure of the intercepted arc.

Answer 2

In your problem, you have an inscribed angle of 31 deg. What does that tell you about the measure of the intercepted arc?

Answer 3

It's 62 degrees?

Answer 4

Yes, correct. The intercepted arc measures 62 degrees.
Now look at the intercpeted arc of 62 degrees and the angle x that you are looking for.

Answer 5

What is the relationship between angle x that you are looking for and the 62-degree arc?

Answer 6

would x be 31?

Answer 7

Correct again. Angle x also intercepts the same arc of 62 degrees, so the measure of x is half of its intercepted arc, so x = 31.

Answer 8

Good job!

Answer 9

thank you so much!

Answer 10

You're very welcome.