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In the diagram above Find the value of ROP

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In the diagram above Find the value of ROP » QuizTablet

In the diagram above Find the value of <ROP

  • A. 85°
  • B. 95°
  • C. 70°
  • D. 110°

QUICK ANSWER…

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…

You may please note these/this:

  • 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.

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

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

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