If O is the centre of the circle, find the value of x in each of the following figures (using the given information):

Question

Asked: March 25, 20212021-03-25T15:23:18+05:30 2021-03-25T15:23:18+05:30In: ICSE

This is circle based question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have figure of circles with constructions and we have to find the value of x using basic properties of circles.

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Understanding ICSE Mathematics
Question no 2

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AAREKH · Answer 1 · 2021-03-27T17:19:02+05:30

∠AOB + ∠AOC + ∠BOC = 360^o

(sum of angles at a point)

∠AOB + 80^o + 130^o= 360^o

∠AOB + 210^o= 360^o

∠AOB = 360^o – 210^o = 150⁰

Now arc AB subtends ∠AOB at the centre ∠ACB at the remaining part of the circle

∠AOB = 2 ∠ACB

∠ACB = ½ ∠AOB = ½ × 150^o = 75^o