Chapter 12.2, Problem 16E

a.

To determine

  $\angle 2$ and $\angle 3$ are corresponding angles. Is the statement true or false?

Answer to Problem 16E

False, $\angle 2$ and $\angle 3$ are not corresponding angles.

Explanation of Solution

Concept used : Two angles that lie between the two parallel lines on opposite side of the transversal line is known as alternate interior angles.

Here, $\angle 2$ and $\angle 3$ lie between the two parallel lines on opposite side of the transversal line. So, they are alternate interior angles not corresponding angles.

b.

To determine

  $\angle 2$ and $\angle 3$ have the equal measure. Is the statement true or false?

Answer to Problem 16E

True, $\angle 2$ and $\angle 3$ have the same measure.

Explanation of Solution

Given information: $\angle 2$ and $\angle 3$ are lie between a parallel line and its transversal line,

Concept Used: Two angles that lie between the two parallel lines on opposite side of the transversal line is known as alternate interior angles and they are always equal.

Here, $\angle 2$ and $\angle 3$ lie between the two parallel lines on opposite side of the transversal line and they are alternate interior angles. So, the value of the $\angle 2$ and $\angle 3$ have the same value.

c.

To determine

  $\angle 2$ and $\angle 3$ complementary angles. Is the statement true or false?

Answer to Problem 16E

True, they are complementary angle.

Explanation of Solution

Given information: $m\angle 3={45}^{\circ }$

Concept used : If the sum of two angles are ${90}^{\circ }$ , they are known as complementary angles.

Calculation:

  $m\angle 2=m\angle 3={45}^{\circ }$ (Alternate interior angles) So, $m\angle 2+m\angle 3={90}^{\circ }$

Therefore, $\angle 2$ and $\angle 3$ complementary angles.

d.

To determine

The sum of measures of angle $\angle 1$ , $\angle 2$ and $\angle 3$ is ${180}^{\circ }$ . Is the statement true or false?

Answer to Problem 16E

False. The sum of measures of angle $\angle 1$ , $\angle 2$ and $\angle 3$ is not ${180}^{\circ }$ .

Explanation of Solution

Given information: $m\angle 1={95}^{\circ }$ , $m\angle 2={45}^{\circ }$ and $m\angle 3={45}^{\circ }$

Concept used : Sum of the angles.

Calculation:

  $m\angle 1+m\angle 2+m\angle 3={95}^{\circ }+{45}^{\circ }+{45}^{\circ }={185}^{\circ }$