Question

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

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

1. if m∠7 = 12x - 12 and m∠3 = 108, solve for x and m∠2.

a. x = ____ b. m∠2 = ____

1. in the figure below, ab∥ef. match the following angle pairs to their vocabulary term.
2. ∠4 and ∠8
3. ∠1 and ∠3
4. ∠8 and ∠5
5. ∠2 and ∠6
6. ∠2 and ∠8

a. alternate exterior angles
b. alternate interior angles
c. consecutive interior angles
d. corresponding angles
e. linear pairs
f. none of these angle pairs
g. same - side exterior angles
h. vertical angles

Explanation:

5.

Step1: Use property of parallel lines

Since \(k\parallel j\), the angles \((6a - 4)\) and \((4a+24)\) are corresponding angles and are equal. So we set up the equation \(6a - 4=4a + 24\).
\[6a-4=4a + 24\]

Step2: Solve the equation for \(a\)

Subtract \(4a\) from both sides: \(6a-4a-4=4a-4a + 24\), which simplifies to \(2a-4=24\). Then add 4 to both sides: \(2a-4 + 4=24+4\), getting \(2a=28\). Divide both sides by 2: \(a=\frac{28}{2}=14\). But this is not in the options. If we assume they are alternate - interior angles (also equal for parallel lines), the equation and solution remain the same. There may be a mis - typing in the problem or options. If we assume they are supplementary (consecutive interior angles), then \((6a - 4)+(4a+24)=180\).
\[6a-4 + 4a+24=180\]
\[10a+20 = 180\]
\[10a=180 - 20=160\]
\[a = 16\]

Step1: Use property of parallel lines

Assume the lines are parallel. \(\angle7\) and \(\angle3\) are corresponding angles (if the lines are parallel), so \(m\angle7=m\angle3\). Set up the equation \(12x-12 = 108\).
\[12x-12=108\]
Add 12 to both sides: \(12x-12 + 12=108+12\), we get \(12x=120\). Divide both sides by 12: \(x = 10\).

Step2: Find \(m\angle2\)

\(\angle2\) and \(\angle3\) are supplementary (linear - pair), so \(m\angle2=180 - m\angle3\). Since \(m\angle3 = 108\), then \(m\angle2=180-108 = 72\).

1. \(\angle4\) and \(\angle8\)

They are corresponding angles as they are in the same relative position with respect to the transversal and the parallel lines.

2. \(\angle1\) and \(\angle3\)

They are vertical angles as they are opposite each other when two lines intersect.

3. \(\angle8\) and \(\angle5\)

They are alternate interior angles as they are between the two parallel lines and on opposite sides of the transversal.

4. \(\angle2\) and \(\angle6\)

They are corresponding angles as they are in the same relative position with respect to the transversal and the parallel lines.

5. \(\angle2\) and \(\angle8\)

They are alternate exterior angles as they are outside the two parallel lines and on opposite sides of the transversal.

Answer:

B. 16

10.