Question 3. (a) In the figure, (i) given below, if ∠DBC = 58° and BD is a diameter of the circle, calculate: (i) ∠BDC (ii) ∠BEC (iii) ∠BAC

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deepaksoniGuru

Asked: March 31, 20212021-03-31T08:20:07+05:30 2021-03-31T08:20:07+05:30In: ICSE

This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have been given that ∠DBC = 58° and BD is a diameter of the circled

And we hve to , calculate:

(i) ∠BDC (ii) ∠BEC (iii) ∠BAC
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Understanding ICSE Mathematics
Question no 3(a)

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AAREKH · Answer 1 · 2021-04-01T06:36:11+05:30

AAREKH Guru

Solution:

(a) ∠DBC = 58°

BD is diameter

∠DCB = 90° (Angle in semi-circle)

(i) In ∆BDC

∠BDC + ∠DCB + ∠CBD = 180°

∠BDC = 180°- 90° – 58° = 32°

ML Aggarwal Solutions for Class 10 Chapter 15 - Image 22

(ii) BEC = 180^o – 32^o= 148^o

(opposite angles of cyclic quadrilateral)

(iii) ∠BAC = ∠BDC = 32^o

(Angles in same segment