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Question

Answer

∠BCA = (180º – 42º) ÷ 2 = 69º  (isosceles ΔABC)

∠ADC = ∠ABC = 42º  (isosceles ΔABD)

∠w = 69º – 42º = 27º

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Useful info….

Exterior angle (d) = sum of 2 opposite interior angles (a + c)

Why?

a + b + c = 180º

b = 180º – (a + c)

 

d = 180º – b

d = 180º – (180º – (a + c))

Therefore, d = a + c

 

Hence, for the question above…

Exterior angle (∠BCA) = ∠w + ∠ADC

69º = ∠w + 42º

∠w = 69º – 42º = 27º

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angle BAC = (180 – 42)/2 = 69 (isosceles triangle)
angle BAD = 180 – 42 x 2 = 96 (isosceles triangle)
angle w = 96 – 69 = 27

Ans : 27 degrees.

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sorry i am wrong

180-84=96

96-69=27

 

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180-42=138

138/2=69

42+42=84

84-69=15

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