Question

In the given figure BE and CE are the bisected of ANGLE ABC and ANGLE ACD show that ANGLE E = 1/2 ANGLE A

Answer 1

<A =180 - 2y - x
y =( 180-x - <A ) / 2 .......(1)
<E = 180- 2x - y
y = (180-2x -E) ....(2)
now equat both eq.
180 - x - A = 2 × (180- 2x - E)
180 - x - A = 360 -4x - 2E
2E - A = 360 - 4x + x =360 -3x
now here first find the value of x
here 3x = 180
x = 60°
now put it on the above eq.
2E -A =360- 3×60 =0
Hence, 2E = A
or, <E = 1/2 of <A