In the Given Below Fig, Rays Oa, Ob, Oc, Op and 0e Have the Common End Point O. Show that ∠Aob + ∠Boc + ∠Cod + ∠Doe + ∠Eoa = 360°. - Mathematics

Advertisements
Advertisements
Answer in Brief

In the given below fig, rays OA, OB, OC, OP and 0E have the common end point O. Show
that ∠AOB + ∠BOC + ∠COD + ∠DOE + ∠EOA = 360°.

Advertisements

Solution 1

Given that

Rays OA, OB, OD and OE have the common end point O.

A ray of opposite to OA is drawn

Since `∠`AOB, `∠`BOF are linear pairs

`∠`AOB + `∠`BOF = 180°

`∠`AOB + `∠`BOC + `∠`COF = 180°

Also

`∠`AOE, `∠`EOF are linear pairs

`∠`AOE + `∠`EOF = 180°

`∠`AOE + `∠`DOF + `∠`DOE = 180°

By adding (1) and (2) quations we get                       

`∠`AOB + `∠`BOC + `∠`COF + `∠`AOE + `∠`DOF + `∠`DOE = 360°

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

Hence proved.

Solution 2

Let us draw AOXa straight line.

∠AOE,∠DOE and ∠DOXform a linear pair. Thus, their sum should be equal to180°.

Or, we can say that:

 ∠AOE +∠DOE +∠DOX  = 180°   (I)

Similarly,, ∠AOB,∠BOC and ∠COXform a linear pair. Thus, their sum should be equal to180°.

Or, we can say that:

 ∠AOB +∠BOC+ ∠COX =  180°       (II)

On adding (I) and (II), we get:

∠AOB +∠BOC + ∠COX +∠DOX +∠AOE +∠DOE = 180°+180°

∠AOB +∠BOC + ∠COD +∠AOE +∠DOE = 360°

Hence proved.

Concept: Introduction to Lines and Angles
  Is there an error in this question or solution?
Chapter 10: Lines and Angles - Exercise 10.2 [Page 14]

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.2 | Q 4 | Page 14

RELATED QUESTIONS

statement are true and false 

If angles forming a linear pair are equal, then each of these angles is of measure 90°.


Fill in the blank so as to make the following statement true:

A ray stands on a line, then the sum of the two adjacent angles so formed is ______


Fill in the blank so as to make the following statement true:

If the sum of two adjacent angles is 180°, then the ______ arms of the two angles are
opposite rays


Define complementary angles.


Define adjacent angles.


Write the complement of an angle of measure x°.


An angle is equal to five times its complement. Determine its measure.


One angle is equal to three times its supplement. The measure of the angle is


In the given figure, if l || m, what is the value of x?


Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. The measure of the smaller angle is


In the given figure, if CP || DQ, then the measure of x is


Write the number of endpoints in
(a) a line segment AB
(b) a ray AB
(c) a line AB


How many rays can be drawn through a fixed point O?


out of \[\overleftrightarrow{AB},\overrightarrow{AB},\overleftarrow{AB}\] and `overline(AB)` which one has a fixed length?


In the given figure, BAC is a straight line.
Find:
(i) x
(ii) ∠AOB
(iii) ∠BOC


Write the complement of 90°


Write the complement of a°


Write the supplement of 100°


Write the supplement of 0°


Write the supplement of (90 + a + b)°


In the given figure, find the measure of the unknown angles:


Share
Notifications



      Forgot password?
Use app×