Question

In the following figure, find the value of x:

Answer 1

∆ACD is isosceles triangle
So,
angle DAC= angle ADC
angle DAC=30°

angle ACD=180°-(30+30)°=>120°
angle ACB=180-120=60°
x=180°-(60+65)°
x=180°-125°
x=55°

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Answer 2

i ) In ∆ACD ,

AC = CD

<CAD = <ADC = 30°

[ Angles opposite to equal sides are

equal ]

ii ) In ∆ACD ,

<ACD + <CDA + <DAC = 180°

[ Angle sum property ]

=> <ACD + 30 + 30 = 180

=> <ACD = 180 - 60 = 120°

iii )In ∆ABC

External angle at C = Sum of interior

opposite angles

120° = <A + <C

=> 120 = 65 + x

=> 120 - 65 = x

=> 55 = x

Therefore ,

x = 55°

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