Question

4. In Fig. 10.34, rays OA, OB, OC, OD and OE have the common end point O. Show that angle AOB + Angle BOC +angle COD+Angle DOE +Angle EOA =360 DEGREE
please answer it's urgent I will mark brainliest​

Answer 1

Given:

In Fig. 10.34, rays OA, OB, OC, OD and OE have the common end point O.

To find:

Show that angle AOB + Angle BOC + angle COD + Angle DOE + Angle EOA = 360 DEGREE

Solution:

Consider the attached figure while going through the following steps.

From given, we have,

The rays OA, OB, OC, OD and OE have the common end point O.

Construction: Draw a ray OP opposite to that of ray OA.

Therefore, we get,

∠ AOB + ∠ BOC + ∠ COP = 180° ..........(1)

(∵ the sum of these angles form a straight line with an angle equal to 180°)

∠ POD + ∠ DOE + ∠ EOA = 180° ..........(2)

(∵ the sum of these angles form a straight line with an angle equal to 180°)

adding (1) and (2), we get,

∠ AOB + ∠ BOC + ∠ COP + ∠ POD + ∠ DOE + ∠ EOA = 180° + 180°

∠ AOB + ∠ BOC + (∠ COP + ∠ POD) + ∠ DOE + ∠ EOA = 360°

as  (∠ COP + ∠ POD) = ∠ COD, we get,

∴ ∠ AOB + ∠ BOC + ∠ COD + ∠ DOE + ∠ EOA = 360°

Hence proved.

Answer 2

Answer:

as all the angles lie around a point

we all know sum of angles around apoint is 360 so simple that is your answer