In a triangle ABC, &ang; BCA = 50&deg;. D and E are points on AB and AC, respectively, such that AD =&nbsp;DE. If F is a point on BC such that BD = DF, then &ang;FDE, in degrees, is equal to&nbsp;

CAT 2021 Question Paper | CAT Verbal Ability Slot 3

Question :

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

Started 1 month ago by Shashank in

0 70

A.
72
B.
80
C.
100
D.
96

Option B is the correct answer.

Explanatory Answer

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