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

Question

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

Manbar Singh · Accepted Answer

(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°