Question

(1) Prove that an exterior angle of a triangle is equal to the sum of its interior
opposite angles. Based on this property find the value of unknown aterior
Angle x.

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Answer 1

by the property of exterior angle of traingle angle x becomes equal to 60 degree

Answer 2

ANSWER.

Given. A ∆ABC in which ∠ACD is an exterior angle.

To prove. ∠ACD = ∠ABC + ∠CAB

Proof. In ∆ABC, by angle-sum property,

∠ABC + ∠CAB + ∠ACB = 180° …(1)

Also, ∠ACB + ∠ACD = 180° …(2)

From (1) and (2),

∠ABC + ∠CAB + ∠ACB =∠ACB + ∠ACD

⇒ ∠ABC + ∠CAB = ∠ACD

Hence, proved.

Now, by exterior-angle property,

x + 60° = 120°

⇒ x = 120° – 60°

⇒ x = 60°

Please mark the BRAINLIEST.

GREETINGS!

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