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°.

☛ Check: Class 9 Maths NCERT Solutions Chapter 6

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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°.

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☛ Related Questions:

• In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
• In Fig. 6.15, ∠PQR = ∠PRQ then prove that ∠PQS = ∠PRT.
• In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
• In Fig. 6.17, POQ is a line. Ray OR, is perpendicular to line PQ. OS another ray lying between rays OP and OR. Prove that ∠ROS = 1/2 (∠QOS - ∠POS).