• 0

Ques 3(b) In the figure (if) given below, AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°. Find: (i) ∠CAD (ii) ∠CBD (iii) ∠ADC

  • 0

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

This ques has been asked in 2008 question paper

In the figure we have AB is parallel to DC, ∠BCE = 80° and ∠BAC = 25°

Niw we have to Find:
(i) ∠CAD (ii) ∠CBD (iii) ∠ADC
ICSE Avichal publication
Understanding ICSE Mathematics
Question 3(b)


1 Answer

  1. (b) in the figure, AB ∥DC

    ∠BCE = 80o and ∠BAC = 25o

    ABCD is a cyclic Quadrilateral and DC is

    Production to E

    ML Aggarwal Solutions for Class 10 Chapter 15 - Image 23

    (i) Ext, ∠BCE = interior ∠A

    80o = ∠BAC + ∠CAD

    80o = 25o + ∠CAD

    ∠CAD = 80o – 25o = 55o

    (ii) But ∠CAD = ∠CBD

    (Alternate angels)

    ∠CBD = 55o

    (iii) ∠BAC = ∠BDC

    (Angles in the same segments)

    ∠BDC = 25o

    (∠BAC = 25o)

    Now AB ∥ DC and BD is the transversal

    ∠BDC = ∠ABD

    ∠ABD = 25o

    ∠ABC = ∠ABD + ∠CBD = 25+ 55o = 80o

    But ∠ABC + ∠ADC = 180o

    (opposite angles of a cyclic quadrilateral)

    80o + ∠ADC = 180o

    ∠ADC = 180– 80o = 100o

    • 0
Leave an answer

Leave an answer


Choose from here the video type.

Put Video ID here: Ex: "sdUUx5FdySs".

Captcha Click on image to update the captcha.

Related Questions