Answer:

c = 126°

Step-by-step explanation:

Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90°

∠POX = ∠POM + ∠MOX

90° = a + b ….(1)

Since a and b are in the ratio 2 : 3 that is,

a = 2x and b = 3x ….(2)

Substituting (2) in (1),

a + b = 90°

2x + 3x = 90°

5x = 90°

x = 90°/5 = 18°

a = 2x = 2 × 18°

a = 36°

b = 3x = 3 × 18°

b = 54°

Also , ∠MOY= ∠MOP + ∠POY

= a + 90° = 36° + 90° = 126°

Lines MN and XY intersect at point O and the vertically opposite angles formed are equal.

∠XON = ∠MOY

c = 126°

I hope you find the answer useful.

Step-by-step explanation:

Sure, I can help you with that.

Given:

* Lines XY and MN intersect at O.

* Angle POY = 90°

* a : b = 2 : 3

To find:

* c

Solution:

1. Since lines XY and MN intersect at O, we know that ∠POY = ∠MOX.

2. We also know that a : b = 2 : 3, so ∠POY = 2x° and ∠MOX = 3x°.

3. Since ∠POY + ∠MOX = 90°, we can substitute in the expressions we found for each angle to get 2x° + 3x° = 90°.

4. Simplifying the right side of the equation, we get 5x° = 90°.

5. Dividing both sides of the equation by 5, we get x° = 18°.

6. Since ∠MOX = 3x°, we know that ∠MOX = 3 × 18° = 54°.

7. Finally, we know that ∠MOX + ∠NOX = 180°, so 54° + c = 180°.

8. Subtracting 54° from both sides of the equation, we get c = 180° - 54° = 126°.

Therefore, c = 126°.

I hope this helps! Let me know if you have any other questions.