Mathematics
happypotato:

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

happypotato:

mhanifa:

What is angle equivalent of arc QS?

happypotato:

the angle equivalent?

mhanifa:

Which angle is same as arc QS?

mhanifa:

Which central angle intercepts the arc QS?

happypotato:

RP is the same

mhanifa:

QOS is same angle

mhanifa:

Can you see any relationship between angles QOS and ROP?

happypotato:

Arent they just opposites?

mhanifa:

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

happypotato:

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

mhanifa:

That's the answer, they are equal

mhanifa:

Now can you see what the answer is?

happypotato:

Awesome! But not really

happypotato:

@mhanifa

mhanifa:

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?

happypotato:

I'm not sure

mhanifa:

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