Question

In fig.6.14, line XY and MN interest at O. if angle POY=90° and a:b = 2:3.find c.​

Answer 1

Solution :

We know that the sum of linear pair are always equal to 180°

So,

∠POY + a + b = 180

Putting the value of ∠POY = 90° (as given in the question) we get,

a + b = 90°

Now, it is given that a : b = 2 : 3 so,

Let a be 2x and b be 3x

2x + 3x = 90°

Solving this we get

5x = 90°

x = 90/5

So, x= 18°

a = 2.x 18° = 36°

Similarly b can be calculated and the value will be

b = 3 x 18° = 54°

From the diagram, b +c also forms a straight angle so,

b + c = 180°

c + 54° = 180°

c = 180° - 54°

c = 126°