Question

Prove that the sum of the angle of a triangle is180

Answer 1

EXPLANATION.

TO PROVE.

GIVEN = ∆ PQR with angle <1 ,<2, <3

PROOF

<1 + <2 + <3 = 180°

CONSTRUCTION.

Draw xy line passing through p parallel to QR.

PROOF.

For line XY or QR with transversal PQ

<2 = <4 = .....(1) [ Alternate angles ]

For line XY or QR with transversal PR

<3 = <5 = .....(2) [ Alternate angles ]

For line XY

<1 + <4 + <5 = 180° [ Linear pairs ]

From equation (1) and (2) we get,

<1 + <2 + <3 = 180°

Hence,

Sum of all angles of triangle = 180°

Note = For figure see image attachment.

Answer 2

To prove :

• $\sf{ \angle1 + \angle2 + \angle3 = 180 \degree}$ ---- i)

Construction :

• Extend BC to D.

Proof :

$\sf{ \rightarrow \: \angle4 = \angle1 + \angle2 }$

Reason :-

Exterior angle = Sum of opposite interior angle

$\sf{ \rightarrow \: \angle3 + \angle4 = 180\degree }$

Reason :-

Linear pair

$\sf{ \rightarrow \: \angle3 + \angle1 + \angle2 = 180\degree}$

Reason :-

From equation i)