Question

in the given figure straight line ab and cd intersect at o.if angle aoc +angle bod =130,then angle aod=?

Answer 1

Given:

AB and CD are straight lines which intersect at O

To find:

∠AOD

Solution:

From the below-attached figure, we can see that,

∠AOC = ∠BOD ...... (i) .... [vertically opposite angles]

But,

∠AOC + ∠BOD = 130° .... (given)

substituting from (i), we get

⇒ ∠AOC + ∠AOC = 130°

⇒ 2∠AOC = 130°

⇒ ∠AOC  = 65° ..... (ii)

Now, we have

∠AOC + ∠AOD = 180° .... [Linear pairs since CD is a straight line]

substituting from (ii), we get

⇒ 65° + ∠AOD = 180°

⇒ ∠AOD = 180° - 65°

⇒ ∠AOD = 115°

Thus, $\boxed{\bold{\angle AOD = \underline{115\°}}}.$

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Also View:

in given figure two straight line AB and CD intersect at a point O. if AOC =42 find the measure of each of thhe angles. i) AOC ii) BOD iii) COB

https://brainly.in/question/3942368

In the given figure, two straight lines AB and CD intersect at a point o. If BOD = 40°, find the measure of each of the angles, BOC, AOC and AOD.​

https://brainly.in/question/9775293

Answer 2

Question :-

In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.

Answer :-

Since AB is a straight line,

∴ ∠AOC + ∠COE + ∠EOB = 180°

or (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)]

or ∠COE = 180° – 70° = 110°

∴ Reflex ∠COE = 360° – 110° = 250°

Also, AB and CD intersect at O.

∴∠COA = ∠BOD [Vertically opposite angles]

But ∠BOD = 40° [Given]

∴ ∠COA = 40°

Also, ∠AOC + ∠BOE = 70°

∴ 40° + ∠BOE = 70° or ∠BOE = 70° -40° = 30°

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

 Plz mrk as brainliest ❤