Question

Prove that the sum of the angles of a triangle is equal to 180° using parallel lines and transversal.


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Answer 1

Answer:

given a b c is a triangle

to prove

angle p + angle q + anger are equal to 180 construction

a b parallel to QR

proof

since ABP is a straight line

angle 1 + angle 2 + angle 3 is equal to 180 degree by linear pair

therefore,angle 1 + angle 2 + angle 3 is equal to 180 degree

angle 4 + angle 2 + angle 5 is equal to 180 degree {angle 1 equal to angle 4

angle 3 equal to angle 5 by alternate angles angle}

p + q + q are equal to 180 degree

sum of interior angle of triangle is 180 degree then proved