Question

1. what is the value of x? 6. angle 1 = 27°. find the measure of angle 4 7. which reason explains why the two lines are parallel? 8. what value of x would make the lines parallel? 9. in a triangle, if you add the 3 angle measurements what do they equal to

Explanation:

5.

Step1: Set angles equal for parallel lines

If lines \(a\) and \(b\) are parallel, the given angles are alternate - interior angles and are equal. So, \(12x−29 = 4x + 1\).

Step2: Isolate variable terms

Subtract \(4x\) from both sides: \(12x-4x−29=4x - 4x+1\), which simplifies to \(8x−29 = 1\).

Step3: Isolate the variable

Add 29 to both sides: \(8x−29 + 29=1 + 29\), getting \(8x=30\).

Step4: Solve for \(x\)

Divide both sides by 8: \(x=\frac{30}{8}=\frac{15}{4}=3.75\).

Step1: Use vertical - angle property

Angle 1 and the angle vertical to angle 2 are equal. Angle 2 and angle 4 are corresponding angles for parallel - like lines (assuming the lines are parallel in the context of angle - relationships). Since vertical angles are equal and corresponding angles are equal for parallel lines, angle 4 is equal to angle 1.

Step1: Recall parallel - line criteria

If the two red - marked angles are equal (alternate - interior angles), then the lines \(p\) and \(q\) are parallel. The reason is the Alternate Interior Angles Theorem which states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the two lines are parallel.

Answer:

\(x = 3.75\)

6.