Question

① In figure 3, if ∠POY = 900

and a : b = 2 : 3, then find the value of c.​

Answer 1

Given :–

• ∠POY = 90°
• a:b = 2:3

To Find :–

• Value of c.

Solution :–

Let, a = 2x and b = 3x

So First, we need to find the value of x.

So,

⟹ ∠POX + ∠POY = 180°

Where,

• ∠POX = a + b = 2x + 3x

So,

⟹ a + b + ∠POY = 180° [Linear Pair]

⟹ 2x + 3x + 90° = 180°

⟹ 5x + 90° = 180°

⟹ 5x = 180° – 90°

⟹ 5x = 90°

⟹ x = $\dfrac{\cancel{90}}{\cancel5}$

⟹ x = 18°

So,

• a = 2x = 2 × 18° = 36°
• b = 3x = 3 × 18° = 54°

Now, we need to find the value of c.

Here, MN is a line, so we can use as a linear pair.

So,

⟹ ∠MOX + ∠XON = 180° [Linear Pair]

• ∠MOX = b = 54°
• ∠XON = c

⟹ b + c = 180°

⟹ 54° + c = 180°

⟹ c = 180° – 54°

⟹ c = 126°

Hence,

The value of c is 126°.

Answer 2

Step-by-step explanation:

Given :–

∠POY = 90°

a:b = 2:3

To Find :–

Value of c.

Solution :–

Let, a = 2x and b = 3x

So First, we need to find the value of x.

So,

⟹ ∠POX + ∠POY = 180°

Where,

• ∠POX = a + b = 2x + 3x

So,

⟹ a + b + ∠POY = 180° [Linear Pair]

⟹ 2x + 3x + 90° = 180°

⟹ 5x + 90° = 180°

⟹ 5x = 180° – 90°

⟹ 5x = 90°

⟹ x = \dfrac{\cancel{90}}{\cancel5}

5

90

⟹ x = 18°

So,

a = 2x = 2 × 18° = 36°

b = 3x = 3 × 18° = 54°

Now, we need to find the value of c.

Here, MN is a line, so we can use as a linear pair.

So,

⟹ ∠MOX + ∠XON = 180° [Linear Pair]

∠MOX = b = 54°

∠XON = c

⟹ b + c = 180°

⟹ 54° + c = 180°

⟹ c = 180° – 54°

⟹ c = 126°

Hence,

The value of c is 126°.