In the figure below, m< ROP = 125°.
2 answers:
Answer:
The measure of the arc RPQ is 205°
Step-by-step explanation:
Given the figure in which
m∠ROP=125°
we have to find the measure of the arc RPQ.
As QP is diameter i.e a straight line therefore
∠1 and ∠2 forms a linear pair hence these angles are supplementary.
By supplementary law
∠1+∠2=180°
∠1+125°=180°
∠1=180°-125°=55°
Now we have to find the measure of the arc RPQ i.e
we have to find the measure of ∠2+∠3
By theorem, angles around a point will always add up to 360 degrees.
∴ ∠1+∠2+∠3=360°
55°+∠2+∠3=360°
∠2+∠3=860-55=205°
Hence, the measure of the arc RPQ is 205°
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