Question

Find the value of angle 'x'.

Answer 1

Step-by-step explanation:

in triangle ABC,

<C = 50°+30° = 80° ( given)

<B = 60°+20°=80° (given )

<A= ?

Now , <A + <B + <C = 180 ° ( angle sum property of ∆)

<A + 80° + 80° = 180°

<A + 160°=180°

<A = 180 ° -160°

<A = 20 °

Now , In ∆AEB ,

<A + <B+ <E = 180° ( angle sum property of triangle )

20° + 20° +<E = 180°

40° + < E = 180°

<E = 180° -40°

<E = 140°

now , in ∆ BCE

<B + < C + < E= 180° ( angle sun property of triangle )

80°+ 80°+ <E =180°

160° +<E = 180°

<E= 180°- 160°

<E= 20°

but , we know , <CEB = < FBE (alternate angles )

similarly , < x = <CBE ( alternate angles )

but , <CBE = 60°

hence , the value of. <x = 60°

therefore , correct answer is 60°