Question

calculate the size of each lettered angle in the following figures

Answer 1

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refer attachment

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Answer 2

Answer:

In the first part the value of x is 44°.

In the second part the value of x is 55°.

Step-by-step explanation:

In the first diagram

As given below .

∠ACB + ∠ACD = 180° (Linear pair)

∠ACD = 108°

∠ACB + 108° = 180°

∠ACB =  180° - 108°

∠ACB =  72°

∠ABE + ∠ABC = 180° (Linear pair)

∠ABE = 116°

∠ABC = 180° - 116°

∠ABC = 64°

Now in ΔABC

∠ABC + ∠ACB + ∠CAB = 180°

64° + 72° + x = 180°

x = 180° - 136°

x = 44°

Therefore the value of x is 44° .

Second part

As given in the diagram given below

∠EDF = ∠ADB = 60°

(By vertically opposite angle property)

Now by using the property the exterior angle is equal to the sum of the opposite interior angle .

∠DBC = ∠ADB + ∠DAB

115° = 60° + x

x = 115° - 60°

x = 55°

Therefore the value of x in the second part is 55° .