Question

lines XY and MN intersect at O. If ∠POY = 90° and a:b = 2 : 3, find c.

Answer 1

Answer:

Angle c is 126.

Explanation:

Given :

• XY and MN intersect at O
• ∠POY = 90°
• a:b = 2 : 3

To Find :

• ∠c

Solution :

Let the common ratio between a and b be x.

∴ a = 2x, and b = 3x

XY is a straight line, rays OM and OP stand on it.

∴ ∠XOM + ∠MOP + ∠POY = 180º

b + a + ∠POY = 180º

3x + 2x + 90º = 180º

5x = 90º

x = 18º

a = 2x = 2 × 18 = 36º

b = 3x = 3 ×18 = 54º

MN is a straight line. Ray OX stands on it.

∴ b + c = 180º (Linear Pair)

54º + c = 180º

c = 180º - 54º = 126º

∴ c = 126º

(Figure in attachment)

Answer 2

$\large \bf Given:-$

• $\sf XY and MN intersect at O$

• $\sf \angle POY = 90 \degree$

• a : b = 2 : 3

$\large \bf To\:Find:-$

• The measure of c

$\large \bf Solution:-$

Let the common ratio between a and b be x

a = 2x ; b = 3x

In the given figure

$\sf \angle POY = 90 \degree$

As the sum angles on a straight line = 180°

$\longrightarrow\sf \angle POX + \angle POY = 180 \degree$

$\longrightarrow\sf \angle POX + 90 \degree = 180 \degree$

$\longrightarrow\sf \angle POX = 180 \degree - 90 \degree$

$\longrightarrow\sf \angle POX= 90 \degree$

$\longrightarrow\sf a + b= 90 \degree$

$\longrightarrow\sf 2x + 3x= 90 \degree$

$\longrightarrow\sf5x= 90 \degree$

$\longrightarrow\sf x= \dfrac{90}{5}$

$\longrightarrow\sf x= 18 \degree$

∠MOX = b = 3x = 3 × 18 = 54°

MON is a straight line

Sum of angles on a straight line = 180°

$longrightarrow \sf \angle MOX + \angle NOX = 180 \degree$

$\longrightarrow \sf 54 \degree + \angle NOX = 180 \degree$

$\longrightarrow \sf \angle NOX= 180 \degree - 54 \degree$

$\longrightarrow \sf \angle NOX = 126 \degree$

Therefore:-

$\large \boxed{ \longrightarrow \bf c = 126 \degree}$