Question

Prove that the sum
of three angles,of a triangle is 180​

Answer 1

The angle sum property of a triangle states that the angles of a triangle always add up to 180°. Every triangle has three angles and whether it is an acute, obtuse, or right triangle, the angles sum to 180°. For example, in triangle ABC, angle A + angle B + angle C = 180°.

Answer 2

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We draw a line parallel to AB that passes

through point C.

Angles C and C' are vertical angles,

therefore ∠C = ∠C'.

Angles B and B' are corresponding angles,

therefore ∠B = ∠B'.

Angles A and A' are corresponding angles, therefore ∠A = ∠A'.

So, the angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.

The three angles A', B', and C' form together a straight angle (they are along the line l).

So, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.

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