Question

1. based on the figure shown, fill in the blanks to make the statements true.

a. angle a and angle ___ are corresponding angles.
b. angle b and angle ___ are alternate exterior angles.
c. angle c and angle ___ are alternate interior angles.
d. angle d and angle ___ are corresponding interior angles.
e. angle f and angle ___ are supplementary angles.
f. angle g and angle ___ are vertical angles.

1. draw parallel lines and a transversal to scale such that a pair of corresponding angles are each 62°. label the measures of the corresponding angles on your figure.

Explanation:

Step1: Recall angle - relationship definitions

Corresponding angles are in the same relative position, alternate interior angles are between the parallel lines and on opposite sides of the transversal, alternate exterior angles are outside the parallel lines and on opposite sides of the transversal, supplementary angles add up to 180 degrees, and vertical angles are opposite each other at an intersection.

Step2: Analyze each pair of angles

a. Angle A and angle D are corresponding angles because they are in the same relative position with respect to the parallel lines and the transversal.
b. Angle B and angle G are alternate exterior angles as they are outside the parallel lines and on opposite sides of the transversal.
c. Angle C and angle F are alternate interior angles since they are between the parallel lines and on opposite sides of the transversal.
d. Angle D and angle F are not corresponding interior angles. There is a mis - statement here. Corresponding angles can be either interior or exterior. Angle D and angle F are not a correct pair for the given description.
e. Angle F and angle H are supplementary angles as they form a linear pair (they are adjacent and their non - common sides form a straight line), so they add up to 180 degrees.
f. Angle G and angle F are vertical angles as they are opposite each other at the intersection of the transversal with one of the lines.

For question 2:

1. Draw two parallel lines, say \(l_1\) and \(l_2\).
2. Draw a transversal \(t\) that intersects \(l_1\) and \(l_2\).
3. Use a protractor to measure and mark a pair of corresponding angles such that each angle is \(62^{\circ}\). Label the angles and the lines as required.

Answer:

1.
a. Angle A and angle D are corresponding angles.
b. Angle B and angle G are alternate exterior angles.
c. Angle C and angle F are alternate interior angles.
d. (There is an error in the statement about angle D and angle F being corresponding interior angles. A correct pair for corresponding angles could be many, for example, if we consider the correct concept, angle A and angle D are corresponding angles).
e. Angle F and angle H are supplementary angles.
f. Angle G and angle F are vertical angles.

1. (Draw two parallel lines and a transversal with a pair of corresponding angles each measuring \(62^{\circ}\) as described above).