Question

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

Answer 1

To Find:-

• The value of x..... ( ? )
• The measure of all angles.... ( ? )

Given:-

∠POR : ∠ROQ which is 5 : 7

Solution:-

Let , ∠POR = 5x and ∠ ROQ = 7x

To get the measure of angle , we need to find the value of x

So,

∠ POR + ∠ ROQ = 180°

( Linear pair of the angles )

➝ 5x + 7x = 180°

➝ 12x = 180

➝ 180/12

➝ x = 15

Now, The angles are:-

∠POQ = 5x

= 5 × 15 = 75°

∠ROQ = 7x

= 7 × 15 = 105°

$Now, \green{Verification}$

We know that a linear Pair measures 180°

So,

75° + 105° = 180°

180 = 180

Hence, Proved

Now,

Since , PQ and RS are intersecting to each other

So, we can tell that,

∠POS = ∠ ROQ =105°

( vertically opposite angles )

∠ SOQ = ∠POR = 75°

( vertically opposite angles )

$Now, \green{Verification}$

We know,that the given diagram measures 360°

as there are two linear pairs

( Linear Pair = 180° )

So,

The angles are :- 75° ; 105° ; 75° and 105°

Now,

75° + 105° + 75° + 105° = 360°

180 + 180 = 360

360 = 360

hence, Proved.

Answer 2

Answer:

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