Question

please answer this question with full explanation
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Answer 1

Answer:

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Answer 2

Step-by-step explanation:

firstly, we use exterior angle property to prove this question

Exterior Angle Property: -If any side of a triangle is extended, then the exterior angle so formed is the sum of the two opposite interior angles of the triangle.

now

In ΔABC, ∠B+∠C = ∠EAB       by Exterior Angle Property      (1)  

              ∠A+∠B = ∠ACD      by Exterior Angle Property      (2)

              ∠A+∠C = ∠CBF      by Exterior Angle Property      (3)

so, from equation (1), (2) and (3) we get

∠A+∠B+∠B+∠C+∠A+∠C = ∠EAB+∠ACD+∠CBF

2(∠A+∠B+∠C) = ∠EAB+∠ACD+∠CBF

we know that sum of all angles of triangle is 180°

so, 2x180° = ∠EAB+∠ACD+∠CBF

  = 360° = ∠EAB+∠ACD+∠CBF

  = 4x90° = ∠EAB+∠ACD+∠CBF

hence proved.