Question

In Fig. 6.14, lines XY and MN intersect at 0. If
POY= 90° and a:b=2:3, find c.​

Answer 1

Answer:

XY perpendicular to PO

angel POY=90

a +b = 90

2x+3x=90

5x=90

x=90/5

x=18

a=2×18=36

b=3×18=54

c = a + POY (vertically oppocite angles)

c = 36 + 90

c = 126

Answer 2

Answer :-

• The measure of ∠c is 126°.

Step-by-step explanation :

To Find :-

• The measure of ∠c

Solution:

Given that,

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

Therefore,

First we need to find out the measure of ∠b,

• ∠a + ∠b + 90° = 180°

Let us assume the the unknown ratio angles as 2x and 3x,

=> ∠a + ∠b + 90 = 180

=> 2x + 3x + 90 = 180

=> 5x + 90 = 180

=> 5x = 180 - 90

=> 5x = 90

=> x = 90/5

=> x = 18

The value of x is 18.

So, the measure of ∠b is, We assumed ∠b as 3x, Therefore,

=> 3x

=> 3*18

=> 54°

Therefore, the measure of ∠b is 54°. Now,

According the question,

• The measure of ∠c is,

=> ∠c + ∠b = 180° .... linear pair

=> ∠c + 54° = 180

=> ∠c = 180 - 54

=> ∠c = 126

Hence,

• The measure of ∠c is 126°.