Question

Z POR: Z ROQ = 5:7, find all the angles.
Example 1: In Fig. 6.9, lines PQ and RS
intersect each other at point O. If​

Answer 1

Step-by-step explanation:

it has given that, 40% of P's income is equal to 75% of Q's income.

Q's income is what percent of P's income.

solution : 40% of P's income = 75% of Q's income

⇒40/100 × P = 75/100 × Q

⇒2/5 × P = 3/4 × Q

⇒8P = 15Q

⇒P/Q = 15/8

here P = 15k, Q = 8k ,where k is proportionality constant.

let Q's income = x % of P's income

⇒8k = x/100 × 15k

⇒800/15 = x

⇒x = 53.33 %

Therefore Q's income is 53.33 % of P's income.

Answer 2

Solution:

∠POR + ∠ROQ = 180° (linear pair of angles)

But,

∠POR : ∠ROQ = 5:7 (Given)

Therefore,

∠POR = 5/12 ×180° = 75°

Similarly,

∠ROQ = 7/12 × 180° = 105°

Now,

∠POS = ∠ROQ = 105° (Vertically opp. angles)

and

∠SOQ = ∠POR = 75° (Vertically opp. angles)