Question

In the following figure, find the value of x:

Answer 1

since,
BD =AD
angleBAD= 50
angleBDA=180-(50+50)=80
angleADC=180-80=100
ad=dc
therefore,180=100+2x
x =40
hope u understand

Answer 2

Solution:

It is given that BD= AD

So, angle DBA = angle BAD [ If two sides are equal in a triangle,they make equal angles]

< DBA = < BAD = 50°

Now in Triangle ∆ ABD

< DBA + < BAD + < ADB= 180° [Angle sum property of triangle]

< ADB = 180°-50°-50°

< ADB = 80°

So, < ADB + < ADC = 180°[linear pair]

< ADC = 180°-80° = 100°

It is given that DC= AD

So, < DAC= < DCA = x° [ If two sides are equal in a triangle,they make equal angles]

Now in Triangle ∆ ADC

< ADC + < DCA + < DAC= 180° [Angle sum property of triangle]

100°+2x= 180°

2x=80°

x= 40°


Hope it helps you.