Question

a student wants to prove that the sum of the angles of triangle abc is 180°. he draws a line, xy, passing through vertex a and parallel to the side bc, as shown. which properties should he use for his proof? m∠xab + m∠yac = 90°, and the measure of alternate interior angles are equal

Explanation:

When a line is drawn parallel to one side of a triangle, alternate - interior angles are equal. Also, the sum of angles on a straight - line is 180°. Here, since \(XY\parallel BC\), \(\angle XAB=\angle ABC\) and \(\angle YAC = \angle ACB\) (alternate - interior angles). And \(\angle XAB+\angle BAC+\angle YAC = 180^{\circ}\) as they are angles on the straight - line \(XY\). So the properties of alternate - interior angles being equal and the sum of angles on a straight - line being 180° are used.

Answer:

The measure of alternate interior angles are equal, and the sum of angles on a straight - line is 180°.