Using the given information, find the value of x in each of the following figures

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deepaksoniGuru

Asked: March 25, 20212021-03-25T14:43:14+05:30 2021-03-25T14:43:14+05:30In: ICSE

This is the basic and conceptual question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this ques we have been given the figure of circle and we have to find the value of x

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Understanding ICSE Mathematics
Question 1

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AAREKH · Answer 1 · 2021-03-27T17:42:34+05:30

AAREKH Guru

Given ∠CPB = 120^o , ∠ACP = 70^o

To find, x^oi,e., ∠PBD

Reflex ∠CPB = ∠BPO + ∠CPA

120⁰= ∠BPD + ∠BPD

(BPD = CPA are vertically opposite ∠s)

2∠BPD = 120^o ∠PBD = 120⁰/2 = 60^o

Also ∠ACP and PBD are in the same segment

∠PBD + ∠ACP = 70⁰

Now, In ∆PBD

∠PBD + ∠PDB + ∠BPD = 180^o

(sum of all ∠s in a triangle)

70⁰+ x^o + 60⁰ = 180^o

x = 180^o– 130^o

x = 50^o