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

**Solution:**

Given: ∠AOC + ∠BOE = 70° and ∠BOD = 40°

To find: ∠BOE , and Reflex ∠COE

We know that vertically opposite angles are formed when two lines intersect and they are equal in measure. Also, sum of the adjacent angles on a straight line is equal to 180 degrees.

Let ∠AOC = x and ∠BOE = y.

Then x + y = 70° ( ∠AOC + ∠BOE = 70°)

Let Reflex ∠COE = z

We can see that AB and CD are two intersecting lines, so the pair of angles formed are vertically opposite angles and they are equal.

i.e, ∠AOD = ∠BOC and ∠AOC = ∠BOD.

Since ∠AOC = x and ∠AOC = ∠BOD = 40°

Thus, we can say that x = 40°.

Also we know that,

x + y = 70°

40° + y = 70°

y = 70° - 40° = 30°

∠BOE = 30°

If we consider line AB and ray OD on it, then ∠AOD and ∠BOD are adjacent angles.

∠AOD + ∠BOD = 180°

∠AOD + 40° = 180°

∠AOD = 180° - 40°

= 140°

Reflex ∠COE = ∠AOC + ∠AOD + ∠BOD + ∠BOE

= 40° + 140° + 40° + 30°

= 250°

Thus, ∠BOE = 30° and the reflex ∠COE = 250°.

**Video Solution:**

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

### NCERT Solutions Class 9 Maths - Chapter 6 Exercise 6.1 Question 1:

**Summary:**

If the given figure lines AB and CD intersect at O, and it is given that ∠AOC + ∠BOE = 70° and ∠BOD = 40°, thus, ∠BOE = 30° and the reflex ∠COE = 250°.