Chapter 3.1, Problem 21WE

a)

To determine

To find: Three pairs of same side interior angles on the same sides of transversals in the given figure and also to find the sum of two angles of pair $m\angle 1$ and $m\angle 2$ .

Answer to Problem 21WE

When lines l and n are intersected by a transversal, then form $\angle 1$ and $\angle 2$ on same interior side of this transversal, so that $m\angle 1+m\angle 2={180}^0$ .

Explanation of Solution

Given information: In below figure, lines l and n are intersected by a transversal, so that on its interior same side, two angles $\angle 1$ and $\angle 2$ form.

  

Concept used: By property of parallel lines, if two parallel lines are cut by a transversal, then the sum of two angles formed on the same side of the transversal between these parallel lines is 180 degree.

Explanation: As it form $\angle 1$ and $\angle 2$ on that same interior side of transversal, so by above rule, their sum will be equal to 180 degree.

  $m\angle 1+m\angle 2={180}^0$

b)

To determine

To find: Three pairs of same side interior angles on the same sides of transversals in the given figure and also to find the sum of two angles of pair $m\angle 3$ and $m\angle 4$ .

Answer to Problem 21WE

When lines l and n are intersected by a transversal, then form $m\angle 3$ and $m\angle 4$ on same interior side of this transversal, so that $m\angle 3+m\angle 4={180}^0$ .

Explanation of Solution

Given information: In below figure, lines l and n are intersected by a transversal, so that on its interior same side, two angles $m\angle 3$ and $m\angle 4$ form.

  

Concept used: By property of parallel lines, if two parallel lines are cut by a transversal, then the sum of two angles formed on the same side of the transversal between these parallel lines is 180 degree.

Explanation: As it form $m\angle 3$ and $m\angle 4$ on that same interior side of transversal, so by above rule, their sum will be equal to 180 degree.

  $m\angle 3+m\angle 4={180}^0$

c)

To determine

To find: Three pairs of same side interior angles on the same sides of transversals in the given figure and also to find the sum of two angles of each pair.

Answer to Problem 21WE

When lines l and n are intersected by a transversal, then form $m\angle 5$ and $m\angle 6$ on same interior side of this transversal, so that $m\angle 5+m\angle 6={180}^0$ .

Explanation of Solution

Given information: In below figure, lines l and n are intersected by a transversal, so that on its interior same side, two angles $m\angle 5$ and $m\angle 6$ form.

  

Concept used: By property of parallel lines, if two parallel lines are cut by a transversal, then the sum of two angles formed on the same side of the transversal between these parallel lines is 180 degree.

As it form $m\angle 5$ and $m\angle 6$ on that same interior side of transversal, so by above rule, their sum will be equal to 180 degree.

  $m\angle 5+m\angle 6={180}^0$

d)

To determine

To find: The information from the given figure that shows that two lines l and n are intersected by a transversal, so that two angles on the same interior angles form there.

Answer to Problem 21WE

When lines l and n are intersected by one or more transversals, the sum of two interior angles on the same side of any of the transversal, always remains equal to 180 degree.

Explanation of Solution

Given information: In below figure, lines l and n are intersected by one or more transversals, so that on its interior same side, different pairs of two angles form.

  

Concept used: By property of parallel lines, if two parallel lines are cut by a transversal, then the sum of two angles formed on the same side of the transversal between these parallel lines is 180 degree.

So, it is concluded that when one or more transversals cut two parallel lines l and n, the sum of two interior angles, forming on the same side of any of the transversal is always equal to 180 degree.