Chapter 2.CT, Problem 1CT

Consider the figure shown at the right.

a) Name the angle that corresponds to $\angle 1$.

b) Name the alternate interior for $\angle 6$.

To determine

a)

To find:

The angle corresponds to $\angle 1$ in the given figure.

Answer to Problem 1CT

Solution:

The $\angle 5$ is corresponds to $\angle 1$.

Explanation of Solution

Given:

The following figure shows the given diagram.

Calculation:

The angles that lie in the same relative positions are called corresponding angles for the given lines. Therefore, $\angle 5$ and $\angle 1$ lie in the same relative positions about the transversal. Therefore, $\angle 5$ corresponds to $\angle 1$.

Conclusion:

Hence, $\angle 5$ corresponds to $\angle 1$.

To determine

b)

To find:

The alternate interior angle for $\angle 6$.

Answer to Problem 1CT

Solution:

The alternate interior angle for $\angle 6$ is $\angle 3$.

Explanation of Solution

Given:

The following figure shows the given diagram.

Calculation:

Alternate interior angles are that angles which have different vertices and lie on the opposite side of the traverse. $\angle 6$ and $\angle 3$ have different vertices and lie on the opposite side of the transverse. Therefore, the alternate interior angle for $\angle 6$ is $\angle 3$.

Conclusion:

Hence, the alternate interior angle for $\angle 6$ is $\angle 3$.