# In the diagram above Find the value of ROP

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• A. 85°
• B. 95°
• C. 70°
• D. 110°

B

## SOLUTION…

There is a rule in circle geometry that states that the sum of opposite angles in a circle quadrilateral = 180 degrees.

That is, if a four-sided quadrilateral is inscribed in a circle as shown in the diagram above, the sum of opposite angles is equal to 180 degrees.

From the diagram,

<OPQ + <ORQ = 180°

Also, <ROP + <RQP = 180°

Therefore, <ROP = 180° – <RQP

But from the diagram, <RQP = 180 – 95 = 85

Therefore, <ROP = 180 – 85 = 95°

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is correct.
3. C is incorrect.
4. D is not the correct answer.
RELATED!  From the diagram above, find the value of OTQ

## KEY-POINTS…

• Always remember that the sum of total angles on a straight line = 180 degrees.
• Sum of opposite angles in a four-sided quadrilateral inscribed in a circle = 180 degrees.

You can also click the golden ASK A QUESTION BOTTON down this page to raise new related questions… OUR COMMUNITY OF EXPERTS WILL BE MORE THAN HAPPY TO TACKLE IT…

/ culled from 2016 JAMB-UTME mathematics past question 9 /

##### In the diagram above Find the value of ROP » QuizTablet

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