Mathematics

In the figure (3) given below, AB || CD. Find the values of x, y and z.

In the figure (3), AB || CD. Find the values of x, y and z. Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Triangles

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Answer

From figure,

In the figure (3), AB || CD. Find the values of x, y and z. Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

∠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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