Question

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Answer 1

Answer:

Angle BCA + Angle CAB = Angle CBD [EXT. ANGLE]

=> Angle CBD = 64°

Angle CBD + Angle BDE = x [EXT. ANGLE]

=> x = 109°

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Answer 2

Answer:

option d :)

Step-by-step explanation:

all the shapes in this figure are triangle.

in ΔABC,

∠A + ∠B + ∠C = 180 -----------------(angle sum property)

34 + ∠B + 30 = 180

64 + ∠B  = 180

∠B  = 180 - 64

∠B  =  116

now, line BC is dividing the line AD into 2 parts so we can use Linear pair formula,

116 + ∠B = 180 --------------------(linear pair)

∠B = 180 - 116

∠B = 64 ----------------------(this ∠B  is in the ΔEBD)

then,in ΔEBD,

∠E + ∠B + ∠D = 180 -----------------(angle sum property)

∠E + 64 + 45 = 180

∠E + 109 = 180

∠E = 71

now,  line ED is dividing the line BC into 2 parts so we can use Linear pair formula,

∠x + ∠E = 180 -----------(linear pair)

∠x + 71 = 180

∠x = 180 - 71

∠x = 109

∴ the answer is ∠x = 109

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