find the size of the lettered angle.
Answers
Answer:
In the first part the value of x is 44°.
In the second part the value of x is 55°.
Explanation:
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° .
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