30. Prove that the sum of three angles of a triangle is 180. Using this result, find the value of x and all three angles of triangle, it the angles are (2x + 7) , (2x- 25)and (3 -12).
Draw a line PQ through the vertex A and parallel to the side BC of a triangle ABC. Now, angle PAB + angle BAC + angle CAQ = 180 degrees (as PQ is a straight line). Equation 1. Angle PAB = angle ABC (as PQ AND BC parallel lines and AB is transversal ;alternate interior angles). ] Equation 2 Angle CAQ = angle ACB (as PQ AND BC parallel lines and AC is transversal ;alternate interior angles). Equation 3 Substitute angle PAB and angle CAQ in Equation 1 by angle ABC and angle ACB (as found in Equation 2 and Equation 3) Thus we get, Angle ABC + angle BAC + angle ACB = 180 degrees. In other words, in the triangle ABC, angle B + angle A + angle C = 180 degrees. Thus the sum of all the angles of a triangle is 180 degrees Proved.