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

• A. 100
• B. 80
• C. 96
• D. 72

Answer 1

The Correct Option is B

We know that, angle on straight line equal to 180°.

so,\( 180-2a+x+180-2b=180\)
\(x-2a-2b+180=0\)
\(x=2a+2b-180…..(1)\)

In \(△ABC, a+b+50=180\)  [ ∴ sum of the angles of triangle=180°]
\(= a+b=130\)

Put the value of a+b in equation (1)
\(x= 2(a-b)-180\)
\(x= 2(130)-180\)
\(x= 260-180\)
\(x=80°\)

∴ The △FDE, in degree, is equal to 80°.

Answer 2

From the triangle ABC,
\(∠A + ∠B + ∠C = 180\degree\)
\(\angle A + \angle B + 50\degree = 180\degree\)
\(∠A + ∠B = 130\degree\)

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