theorem:- sum of the angle of a triangle is 160°.
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Correction in the question :
Some of the angles of triangle is 180°.
Statement : The sum of the angles of a triangle is 180°.
To prove : sum of the angles of ΔABC is 180°
Construction : Draw a line parallel to BC.
Proof :
Since lm || BC, we have ;
∠2 = ∠y ..... (i) . [Alternate interior angles]
Similarly,
∠1 = ∠z ....... (ii) . [Alternate interior angles]
Also, sum of angles at a point a on line is 180°.
∴ ∠2 + ∠x + ∠1 = 180°
⇒ ∠y + ∠x + ∠z = 180°
⇒ ∠x + ∠y + ∠z = 180°
⇒ ∠A + ∠B + ∠C = 180°
Therefore,
Sum of all angles of a Δ is 180°
Some of the angles of triangle is 180°.
Statement : The sum of the angles of a triangle is 180°.
To prove : sum of the angles of ΔABC is 180°
Construction : Draw a line parallel to BC.
Proof :
Since lm || BC, we have ;
∠2 = ∠y ..... (i) . [Alternate interior angles]
Similarly,
∠1 = ∠z ....... (ii) . [Alternate interior angles]
Also, sum of angles at a point a on line is 180°.
∴ ∠2 + ∠x + ∠1 = 180°
⇒ ∠y + ∠x + ∠z = 180°
⇒ ∠x + ∠y + ∠z = 180°
⇒ ∠A + ∠B + ∠C = 180°
Therefore,
Sum of all angles of a Δ is 180°
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prove that sum of all angle is 160
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