SarkariPYQ

SSC CPO 2019 PYQ — Question 137

SSC CPO Tier I - 12th December 2019 - Shift 1 • Quantitative Aptitude • Q137

Back to paper

ABCD is a cyclic quadrilateral. Sides AB and DC when produced meet at E, and sides BC and AD, when produced, meet at F. If ∠BFA = 60° and ∠AED = 30°, then the measure of ∠ABC is?

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option  2 i.e. 75

Application

Given that ABCD is a cyclic quadrilateral. Sides AB and DC, when produced, meet at E, and sides BC and AD, when produced, meet at F. If ∠BFA = 60o and ∠AED = 30o as shown in the figure below

Figure for the explanation of question 137

∠ADC = 180° - ∠ABC  (Sum of opposite angles of a cyclic quadrilateral is 180°)………………..(1)

∠BCD = 180° - ∠BAD (Sum of opposite angles of a cyclic quadrilateral is 180°)………………(2)

Also, ∠ADC + ∠FDC = 180° (linear pair)

So, ∠FDC = 180° - ∠ADC

From (1)

∠FDC = ∠ABC………………(3)

Now, ∠BCD+ ∠FCD =180° (linear pair)

So, ∠FCD = 180° - ∠BCD

From (2)

∠FCD = ∠BAD………………(4)

In triangle FDC

∠FDC + ∠FCD + ∠DFC = 180°

∠ABC + ∠BAD + 60° = 180°

∠ABC + ∠BAD = 120°……………………….(5)

In triangle AED

∠EAD + ∠ADE + ∠AED = 180°

180° - ∠BAD +  ∠ABC = 180° - 30°

∠BAD - ∠ABC = 30°

Subtract (6) from (5)

2∠ABC = 150°

∠ABC = 75°