Question

In the figure below, ∠mROP = 125°.



Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.

mQS

Answer 1

What is angle equivalent of arc QS?

Answer 2

the angle equivalent?

Answer 3

Which angle is same as arc QS?

Answer 4

Which central angle intercepts the arc QS?

Answer 5

RP is the same

Answer 6

QOS is same angle

Answer 7

Can you see any relationship between angles QOS and ROP?

Answer 8

Arent they just opposites?

Answer 9

Do you know how is it called? They are vertically opposite angles.
Do you know their relationship, like which one is greater or not?

Answer 10

I don't think i do know. I thought they were equal

Answer 11

That's the answer, they are equal

Answer 12

Now can you see what the answer is?

Answer 13

Awesome! But not really

Answer 14

@mhanifa

Answer 15

You have:
∠mROP = ∠mQOS as vertical angles
Also you have:
∠mQOS = mQS as central angle is equal to intercepted arc measure:
Also you have:
∠mROP = 125°
No can you find the measure of mQS?

Answer 16

I'm not sure

Answer 17

Ok, use this tip:
If a = b and b = c you can say that a = c