Question

please answer the question​

Answer 1

Answer:

Ray BO is the bisector of ∠ CBE.

Therefore, ∠ CBO = 1/2 ∠ CBE

= 1/2  (180° – y)

= 90° – 2y/2               (1)

Similarly, ray CO is the bisector of ∠ BCD.

Therefore, ∠ BCO = 1/2∠ BCD

2 (180° – z)

= 90° – z/2               (2)

In ∆ BOC, ∠ BOC + ∠ BCO + ∠ CBO = 180° (3)

Substituting (1) and (2) in (3), you get

∠ BOC + 90° – z/2+90° –y/2=180°

So, ∠ BOC = z/2+y/2

or, ∠ BOC = 1/2(y + z) (4)

But, x + y + z = 180° (Angle sum property of a triangle)

Therefore, y + z = 180° – x

Therefore, (4) becomes          

                                      ∠ BOC = 1/2 (180° – x)

= 90° – x/2

= 90° – 1/2∠ BAC

hence prooved

hope it helps