CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 5 : In a triangle ABC , ∠ BCA =50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then ∠ FDE, in degrees, is equal to

Video Explanation

Explanatory Answer

We draw the diagram carefully with the given information.

From the triangle ABC,
∠A + ∠B + ∠C = 180⁰
∠A + ∠B + 50⁰ = 180⁰
∠A + ∠B = 130⁰
In the quadrilateral CFDE,
∠C + ∠F + ∠D + ∠E = 360⁰
50⁰ + 180⁰ - ∠A + ∠x + 180⁰ - ∠B = 360⁰
50⁰ + ∠x = ∠A + ∠B
50⁰ + ∠x = 130⁰
∠x = 80⁰
∠FDE = 80⁰

The question is " In a triangle ABC , ∠ BCA =50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then ∠ FDE, in degrees, is equal to "

Hence, the answer is '80'

Choice B is the correct answer.