Question

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Answer 1

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answer:-

a) 50 degree

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Answer 2

Answer:

50 (a)

Step-by-step explanation:

Consider the ΔABC. ACD is the exterior angle and BAC and ABC are interior angles.

So, ACD = BAC+ABC (According to triangle property)

Or, ACD -ABC = BAC ———–(i)

Now, consider the ΔBCE,

ECD = EBC+BEC

Or, BEC =ECD - ECB

We know that BE and EC bisect ABC and ACD respectively.

So, ACD = 2 ECD and ABC = 2EBC

Now, BEC = ½ ACD – ½ABC

Or, BEC = ½ (ACD -ABC)

From (i) we know that ACD -ABC = BAC

So, BEC = ½ BAC (hence proved).