Question

prove that sum of angle of a triangle is opposite two right angle .

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.

(The Elements: Book I: Proposition 32)

Proof

Euclid-I-32.png

Let △ABC be a triangle.

Let BC be extended to a point D.

From External Angle of Triangle equals Sum of other Internal Angles:

∠ACD=∠ABC+∠BAC

Bby by Euclid's Second Common Notion:

∠ACB+∠ACD=∠ABC+∠BAC+∠ACB

But from Two Angles on Straight Line make Two Right Angles, ∠ACB+∠ACD equals two right angles.

So by Euclid's First Common Notion, ∠ABC+∠BAC+∠ACB equals two right angles.