Question

to verify that sum of exterior angle of a triangle is 360

Answer 1

See the attachment :)
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Let ABC is a triangle

∠A = 1, ∠B = 2 and ∠C = 3

Sum of interior angles of a triangle = 180

∠1 + ∠2 + ∠3 = 180

∠1 + ∠a = 180 (L•P)

∠2 + ∠b = 180 (L•P)

∠3 + ∠c = 180 (L•P)

Therefore From Figure :-

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∠1 + ∠a + ∠2 + ∠b + ∠3 + ∠c = 180° + 180° + 180

180°+ ∠a + ∠b + ∠c = 540°

∠a + ∠b + ∠c = 540° – 180° = 360

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Exterior angles of a triangle is 360

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Regards :)

Cybary

Be Brainly :)

Answer 2

Heya

Let the exterior angles of traingle be angle A, angle B and angle C

Let the interior angles of the traingle be angle 1, angle 2 and angle 3.

We know that sum of interior angles of triangle is 180°

Angle 1+ angle A = 180°.....(1)

Angle 2+ angle B = 180°.....(2)

Angle 3+ angle C = 180°....(3)

(1) + (2) + (3)

Angle 1+ angle 2 + angle 3 + angle A + angle B + angle C = 180+180+180

180+ angle A + angle B + angle C = 540

angle A + angle B + angle C = 540-180=360

Hence proved.