Question

In the given figure, prove that the sum of all angles around the point O is 360

Answer 1

Step-by-step explanation:

To prove : Sum of all the angles around the point O is 360°. I.e, we have to provide that :

» POQ + ∠POS + ∠QOR + ∠SOR = 360°

Construction : Make a ray OA originating from point O.

Here,

• ∠POQ and ∠POA are forming linear pair.

$\longrightarrow \sf{\quad {\angle POQ + \angle POA = 180^\circ \dots 1) }}$

Also,

• ∠QOR and ∠AOR are forming linear pair.
• ∠AOR = ∠AOS + ∠SOR

$\longrightarrow \sf{\quad {\angle QOR + \angle AOR = 180^\circ }}$

$\longrightarrow \sf{\quad {\angle QOR + \angle AOS + \angle SOR = 180^\circ dots 2)}}$

Adding both the equations (1) and (2).

↠∠POQ + ∠POA + ∠QOR + ∠AOS + ∠SOR = 180° + 180°

• ∠AOS + ∠POA = ∠POS

↠∠POQ + ∠POA + ∠AOS + ∠QOR + ∠SOR = 360°

↠∠POQ + ∠POS + ∠QOR + ∠SOR = 360°

$\large {\underline { \sf {Hence \; proved!!}}}$

$\rule{200}2$

Learn More :

• The sum of all the angles around a point is 360°.

• The sum of all the angles lie on a straight line is 180°.

• Measure of complete angle is 360°.

• Measure of straight angle is 180°.

• Measure of right angle is 90°.

• Measure of acute angle is more than 0° but less than 90°.

• Measure of obtuse angle is more than 90° but less than 180°.

• Measure of reflex angle is more than 180° but less than 360°.