Question

The sum of measures of two alternate interior angles of two parallel lines with a transversal is 210°. What are the possible measures of the angles formed by the parallel lines and the transversal?

Answer 1

Solution-

If the lines are parallel, then the alternate interior angles are congruent.

As the sum of measures of the two alternate interior angles = 210°

⇒ Measure of one alternate interior angles = 105°

$So \ m\angle 1 = m\angle3=105^{\circ}= m\angle5= m\angle 7$

Since a straight angle contains 180º, the two angles forming a linear pair also contain 180º when their measures are added (making them supplementary).

$So \ m\angle 1 + m\angle2 = 180^{\circ},m\angle 3 + m\angle4 = 180^{\circ},m\angle 5+ m\angle6 = 180^{\circ} \ and \ m\angle 7 + m\angle8 = 180^{\circ}$

$So \ m\angle 2= 75^{\circ}, m\angle4=75^{\circ}, m\angle 6=75^{\circ} \ and \ m\angle 8=75^{\circ}$