Exercise 6th 1

1. In Fig. 6.13, lines AB and CD intersect at O. If AOC +BOE = 70° and BOD = 40°, find BOE and reflex COE.

Solution:

From the diagram, we have

(AOC +BOE +COE) and (COE +BOD +BOE) forms a straight line.

So, AOC+BOE +COE = COE +BOD+BOE = 180°

Now, by putting the values of AOC+BOE = 70° and BOD = 40° we get

COE = 110° and

BOE = 30°

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

Solution:

We know that the sum of a linear pair is 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°

So, x = 18°

∴ a = 2×18° = 36°

Similarly, b can be calculated and the value will be

b = 3×18° = 54°

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

b+c = 180°

c+54° = 180°

∴ c = 126°