Question

HELP ME PLEASE!!! I looked it up and everything and I still can’t find it!

Answer 1

First option is the correct answer.

Angle RNQ is equal in measure to arc PR

Explanation:

From the figure we get, central angle of arc PR is 120°

That is, <POR = 120°

To find m<RON

We know that,

<POR and <RON are linear pair.

Sum of linear pair angles is 180°

m<POR + m<RON = 180°

m<RON = 180 - m<POR = 180 - 120 = 60°

To find m<RNQ

It is given that,

OR = RN, therefore <RON = <RNO = 60°

Again <RNO and <RNQ are linear pair.

m <RNO + m<RNQ = 180°

m<RNQ = 180 - m<RNO = 180 - 60 = 120°

m<RNQ = 120°

Therefore the correct answer is first option

Answer 2

Answer: Angle RNQ is equal the measure of arc PR.

Explanation:

Since, by the given diagram,

RO = RN = ON ( Radius of the circle )

⇒ Triangle RON is an equilateral triangle,

⇒ m∠RNO = 60° ( By the property of equilateral triangle)

But m∠RNQ = 180° - m∠RNO ( Linear pairs )

⇒ m∠RNQ = 180° - 60° = 120°

Also, it is given that m( arc PR ) = 120°

⇒ Measure of arc PR = measure of angle RNQ,

⇒ First option is correct.