Question

Prove with reason that if we produce one side of a triangle then the measurement of the exterior angle is sum of the measurement of two opposite interior angles.​

Answer 1

Step-by-step explanation:

In △ABC,

∠a=∠ABC+∠ACB (Exterior angle property)

∠b=∠ACB+∠BAC (Exterior angle property)

∠C=∠ABC+∠BAC (Exterior angle property)

Adding all the equations:

∠a+∠b+∠c=2(∠ABC+∠ACB+∠BAC)

∠a+∠b+∠c=2(180

o

)

∠a+∠b+∠c=360

∘

.

Therefore, option B is correct.

Answer 2

Given:

• In ∆ ABC, side BC is produced to D and ACD is the exterior angle formed..

• ABC and BAC are the interior opposite angles.

To prove:

• ACD=ABC+BAC

Proof:

$\sf \: : \implies \:ABC+BAC+ACB \: = 180°...(i) (Theorem)$

$\sf \: : \implies \:Also \: ACB+ACD = 180°...(ii)(Linear pair)$

$\sf \: From (i) \: and \: (ii) \: equ$

$\sf \:: \implies \: ABC+BAC+ACB-ACB+ACD-ACB$

Subtract ACB from both sides,

$\\ \sf : \implies \: ABC+BAC-ACD$