Mathematics
In the figure (3) given below, AB || CD. Find the values of x, y and z.
Triangles
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Answer
From figure,
∠BAD = ∠ADC (Alternate angles)
∴ x = 42°
In △CED,
⇒ 24° + ∠CED + 42° = 180°
⇒ ∠CED + 66° = 180°
⇒ ∠CED = 114°.
From figure,
⇒ ∠CEA + ∠CED = 180°
⇒ ∠CEA + 114° = 180°
⇒ ∠CEA = 66°.
In △CEA,
⇒ y = ∠CEA = 66° (As angles opposite to equal sides are equal)
In △CEA,
⇒ z + y + ∠CEA = 180°
⇒ z + 66° + 66° = 180°
⇒ z + 132° = 180°
⇒ z = 48°.
Hence, x = 42°, y = 66° and z = 48°.
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