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

Answer: (B)

80

Answer 2

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°.