Prove that, sum of the measures of all angles of a triangle PQR is 180⁰.
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Given :
A triangle ABC.
To prove :
∠A+∠B+∠C=180
o
⟹∠1+∠2+∠3=180
o
Construction :
Through A, draw a line l parallel to BC.
Proof :
Since l∥BC. Therefore,
∠2=∠4
And, ∠3=∠5
adding eq(i)and(ii)
Therefore, ∠2+∠3=∠4+∠5
∠1+∠2+∠3=∠1+∠4+∠5 [adding∠1bothSide]
∠1+∠2+∠3=180o
Thus, the sum of three angles of a triangle is 180o.
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