Question

in the given figure , side ca of∆abc has been produced to e. if ac=ad=bd;angle acd =46°and angle bae=x°. find the value of x.​

Answer 1

Step-by-step explanation:

Given : AC = AD = BD

Soln.:

In ∆ABC

AC = AD { Given }

then , Angle C = Angle D { Since the opposite sides are equal , the opposite angles are also equal }

Angle D = 46°

Now , Angle D + Angle DAC + Angle A = 180° { Property of a ∆ }

Then , Angle DAC = 180° - 92°

=> 88°

Now , Angle BDA = 180° - 46° = 134° { Linear pair }

Similarly , In ∆ABD

AD = BD { Given }

Let , Angle A = Angle B = y

So , y + y + Angle BDA = 180° { Property of a ∆ }

So , y = 46/2 = 23°

Hence ,

Angle X + Angle BAD + Angle DAC = 180° { Angles on a straight line }

So , Angle X = 180° -111°

=> 69°