Question

In Fig. 8.47, lines PQ and RS intersect each other at point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

Answer 1

∠POR = ∠QOS = 75°( vertically opposite angles)

∠ ROQ = ∠POS = 105° ( vertically opposite angles)

Step-by-step explanation:

Given :  ∠POR : ∠ROQ = 5 : 7

Let ∠POR = 5x & ∠ROQ = 7x

By Linear pair axiom,

∠POR + ∠ROQ = 180°

5x + 7x = 180°

12x = 180°

 x = 180/12

x = 15°  

so,

∠POR = 5x = 5 × 15 = 75°

∠ROQ =  7x = 7 × 15 = 105°

then,

∠POR = ∠QOS = 75°( vertically opposite angles)

∠ ROQ = ∠POS = 105° ( vertically opposite angles)

Linear pair of angles:

If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.

Hope this answer will help you…..

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Answer 2

let x be the ratio between the angles

• 5:7 = 5x and 7x

then,

5x + 7x = 180° [Linear pair]

=> 12x = 180°

=> x = 180/12

=> x = 15°

so,

• 5x = 5 × 15 = 75°
• 7x = 7 × 15 = 105°

then,

angle POR = QOS ( VERTICALLY OPPOSITE ANGLES)

angle QOR = SOP ( VERTICALLY OPPOSITE ANGLES)