Can you prove that the angel of a triangle is equal to 180⁰
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In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn). A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
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Refers to the above attachment
A ΔABC
To Prove:- ∠A + ∠B + ∠C = 180°
∠1 + ∠2 + ∠3 = 180°
Construction:- Through A draw lm II BC
Proof:- Since, lm II BC
Therefore, ∠2 = ∠4 .... eq(i)
∠3 = ∠5 .... eq(ii)
Adding, eq(i) and eq(ii), we get
∠2 + ∠3 = ∠4 + ∠5
Adding ∠1 both side, we get
∠1 + ∠2 + ∠3 = ∠1 + ∠4 + ∠5
∠1 + ∠2 + ∠3 = 180°
thus, the sum of all interior angles of a triangle is equal to 180°.
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