Question

check the image ,,,,,,,,,​

Answer 1

Answer:

angle POR= 75

angle ROQ=105

angle POS=15

angle SOQ=15

Answer 2

Answer:

angles are 75° and 105°

Step-by-step explanation:

Well This a bit long but it's ok

The lines pq and rs intersect at point O

At point O the sum of the angles is 360° (Since one whole point has 360° as sum)

And another info we can derive is that angles ∠POR and ∠SOQ are vertically opposite angles(equal to each other)

Similarly ∠ROQ and ∠POS are also vertically opposite hence Equal to each other

So this all what we know now :--

Sum of 4 angles=360°

∠POR = ∠SOQ

∠ROQ = ∠POS

And

Since ∠POR : ∠ROQ = 5:7

∴ ∠POR : ∠ROQ = ∠SOQ : ∠POS = 5:7

∴ ∠POR + ∠ROQ + ∠SOQ + ∠POS =360°

Let The angles be 5x and 7x = 5:7

⇒ 5x + 7x + 5x + 7x =360°

⇒24x = 360°

⇒ x = 360°/24 = 15°

So x = 15

∠POR = ∠ROQ = 5x = 5*15° = 75°

∠ROQ = ∠POS = 7x = 7*15° = 105°

we can also prove it by

75+75+105+105 =360

Hence proved