Question

1. in the diagram, k || j. what is the value of a? a. 12 b. 16 c. 35 d. 73 10. if m∠7 = 12x - 12 and m∠3 = 108, solve for x and m∠2. a. x = __ b. m∠2 = __ 11. in the figure below, (overline{ab}paralleloverline{ef}). match the following angle - pairs to their vocabulary term. 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 1. ∠4 and ∠8 2. ∠1 and ∠3 3. ∠8 and ∠5 4. ∠2 and ∠6 5. ∠2 and ∠8

Explanation:

5.

Step1: Use the property of corresponding angles

Since \(k\parallel j\), the corresponding angles are equal. So \(6a - 4=4a + 24\).

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 there is no 14 in the options. Let's assume they are alternate - interior angles (also equal for parallel lines), and the equation still holds.

Step1: Use the property of corresponding angles

\(\angle7\) and \(\angle3\) are corresponding angles for parallel lines. So \(12x-12 = 108\).

Step2: Solve for \(x\)

Add 12 to both sides of the equation: \(12x-12 + 12=108 + 12\), we get \(12x=120\). Divide both sides by 12: \(x = 10\).

Step3: 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 \(\angle8\) are corresponding angles.
2. \(\angle1\) and \(\angle3\) are vertical angles.
3. \(\angle8\) and \(\angle5\) are consecutive interior angles.
4. \(\angle2\) and \(\angle6\) are corresponding angles.
5. \(\angle2\) and \(\angle8\) are alternate - interior angles.

Answer:

There seems to be an error in the problem or options as the correct value of \(a = 14\) is not listed.

10.