Q. Find unknown sizes of the angles.

Soln: 

<PQR = <QRS [∵ PQ || RS, being alternate angles]

 or, y = 2x

From r PQR,

<PQO + <OPQ = <POR

[∵ an exterior angle of a triangle is equal to the sum of the opposite interior angles.]

[Some books prefer to write: External property of a triangle]

x + y = 87⁰

x + 2x = 87⁰

x = 29⁰

y = 2x = 2 * 29⁰ = 58⁰

and 2x = 2 * 29⁰ = 58⁰

Hence, <SPQ = 29⁰, <PQR = 58⁰ and <SRQ = 58⁰

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