Chapter 11.1, Problem 32IP

To determine

To find: Conclude that both pairs of opposite sides of the quadrilateral are parallel.

Answer to Problem 32IP

line $p$ and line $q$ are parallel

line $r$ and line $s$ are not parallel

Explanation of Solution

Given information:

Lines $p,q,r$ and $s$ forms a quadrilateral.

From the given figure

We can say that

For the two lines $p$ and line $q$

Given exteriors angles are ${60}^0$ and ${120}^0$

Their sum is ${60}^0+{120}^0={180}^0$

If two parallel lines are intersected by a transversal then the sum of exterior angles is ${180}^0$ and its converse also holds

Therefore, using above statement

We can say that line $p$ and line $q$ are parallel

For the two lines $r$ and line $s$

Given exteriors corresponding angles are ${60}^0$ and ${62}^0$

As ${60}^0\ne {62}^0$

If two parallel lines are intersected by a transversal then the Corresponding angles are equal and its converse also holds.

Therefore, using above statement

We can say that line $r$ and line $s$ are not parallel

Therefore,

We can say that

line $p$ and line $q$ are parallel

line $r$ and line $s$ are not parallel