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CAT 2021 Slot 3 QA Question & Solution

GeometryMedium

Question

If a triangle ABC, $\angle BCA=50^{0}$. 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 $\angle FDE$, in degrees, is equal to

Options

72
80
100
96

Solution

Question Figure

We need to find out p.

Angle ADE = 180 - 2x

Angle BDF = 180 - 2y

Now, 180 - 2y + p + 180 - 2x = 180 [Straight line = 180 deg]

p = 2x + 2y - 180

Also, x + y + 50 = 180 [Sum of the angles of triangle = 180]

x + y = 130

p = 260 - 180 = 80 degrees.