Question

version 1
name: inigo gonzales
use the picture to the right to answer questions 1 - 4.

1. which angles are vertical angles?

a. ∠1 and ∠2 b. ∠1 and ∠3 c. ∠1 and ∠4 d. ∠1 and ∠6

1. which angles are alternate exterior angles?

a. ∠2 and ∠7 b. ∠3 and ∠8 c. ∠4 and ∠8 d. ∠5 and ∠3

1. which angles are alternate interior angles?

a. ∠7 and ∠8 b. ∠6 and ∠3 c. ∠2 and ∠3 d. ∠1 and ∠4

1. which angles are corresponding angles?

a. ∠1 and ∠3 b. ∠1 and ∠4 c. ∠7 and ∠6 d. ∠1 and ∠8

1. in the diagram, k || j. what is the value of a?

a. 12 b. 16 c. 35 d. 73

Explanation:

Step1: Recall angle - pair definitions

Vertical angles are opposite each other when two lines intersect. Alternate exterior angles are outside the two lines and on opposite sides of the transversal. Alternate interior angles are inside the two lines and on opposite sides of the transversal. Corresponding angles are in the same relative position with respect to the lines and the transversal.

Step2: Answer question 4

Corresponding angles are in the same relative position. For parallel - line and transversal scenarios, ∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 are corresponding angles. So for the given options, ∠1 and ∠5 is not in the options, but ∠1 and ∠8 are corresponding angles.

Step3: Answer question 5

Since k || j, the angles (5a - 4) and (4a+24) are corresponding angles and are equal.
Set up the equation:
\[5a−4 = 4a + 24\]
Subtract 4a from both sides:
\[5a-4a−4=4a - 4a+24\]
\[a−4 = 24\]
Add 4 to both sides:
\[a=24 + 4=28\]
However, if we assume they are alternate interior or exterior angles (which are also equal for parallel lines), the equation and solution are the same.

Answer:

1. D. ∠1 and ∠8
2. None of the given options (correct answer is 28)