prove that sum of the angles of a triangle is 180 degrees .If in the triangle ABC angle A +angle B=120 degrees and angles B+angle C=100 degrees. find angle B

(1).

GIVEN:   ABC is a .



TO PROVE:    A + B + C = 180°CONSTRUCTION:      Draw a line XY parallel to BC.PROOF:    Since  XY  BC and AC is a transversal,YAC = ACB   Alternate Interior Angles  .............1Since  XY  BC  and AB is a transversal,XAB = ABC   Alternate Interior Angles  .............2Now, at point A, YAB and XAB form a linear pair. So,   YAB + XAB = 180°YAC + BAC + XAB = 180°ACB + BAC +ABC =  180° C + A + B = 180° A + B +  C = 180°  

(2).



In  ABC,      A + B  = 120°   Given       A = 120° - B  ............1Also, B + C = 100°    Given    C = 100° - B  ............2Now,      A + B + C = 180°    Angle Sum Property 120° - B + B + 100° - B = 180°    Using 1 & 2 220° - B = 180° B = 220° - 180° B = 40°

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Consider a triangle PQR and 1, 2 and 3 are the angles of ΔPQR (figure shown below). We need to prove that 1 + 2 + 3 = 180o.

XPY is a line.∴4 + 1 + 5 = 180o(1)But XPY || QR and PQ, PR are transversals.So, 4 = 2 and 5 = 3(Pairs of alternate angles)Substituting 4 and 5 in (1), we get2 + 1 + 3 = 180o∴1 + 2 + 3 = 180o

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