Madhya Pradesh Police Exam Model Paper 3

Question : 54 of 100

Marks: +1, -0

ABC is a triangle and its side AB, BC and CA are produced to E, F and G respectively. If ∠CBE = ∠ACF = 130°. Find ∠GAB.

Solution:

We know that

∠ABC + ∠CBE = 180°

∠ACB + ∠ACF = 180°

Given,

∠CBE = ∠ACF = 130°

∴ ∠ABC = 180° - ∠ CBE

= 180 – 130

= 50°

∠ACB = 180 - ∠ ACF

= 180 – 130

= 50°

Sum of interior angles of a triangle = 180°

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 100° + ∠BAC = 180°

⇒ ∠BAC = 80 °

∠BAC + ∠GAB = 180°

⇒ ∠GAB = 100°

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