Question

solve for x to make a||b.
a
b
x = ?

Explanation:

Step1: Identify vertical angles

The angle adjacent to \(60^\circ\) is vertical to \((8x + 8)^\circ\), so they are equal.

Step2: Set up equation

The adjacent angle and \(60^\circ\) form a straight line: \(8x + 8 + 60 = 180\)

Step3: Simplify equation

Combine constants: \(8x + 68 = 180\)

Step4: Solve for x

Subtract 68: \(8x = 112\); divide by 8: \(x = 14\)? Wait, no—wait, if lines A||B, the angles are corresponding or supplementary? Wait correction: If A||B, the angles are supplementary? No, wait the angle next to \(60^\circ\) is \(180-60=120^\circ\), which equals \(8x+8\). So \(8x+8=120\)

Step5: Correct equation

\(8x + 8 = 120\)

Step6: Solve for x

Subtract 8: \(8x=112\); \(x=14\)? Wait no, wait 120-8=112, 112/8=14. Yes, that's right. Wait initial mistake was wrong angle relation. Correct: When lines are parallel, the angles are equal (vertical or corresponding). The angle supplementary to \(60^\circ\) is equal to \(8x+8\). So \(8x+8=120\), so \(x=14\). Wait why did I think 8 earlier? No, 120-8=112, 112/8=14. So final answer is 14.

Wait correction again: Let's do it properly. The angle next to \(60^\circ\) is \(180-60=120^\circ\). Since A||B, this angle is equal to \((8x+8)^\circ\) (corresponding angles). So:

\(8x + 8 = 120\)

Subtract 8: \(8x = 112\)

Divide by 8: \(x = 14\)

Yes, that's correct. So the answer is 14.

Step1: Find supplementary angle

Angle adjacent to \(60^\circ\): \(180 - 60 = 120^\circ\)

Step2: Set equal to given angle

\(8x + 8 = 120\)

Step3: Solve for x

Subtract 8: \(8x = 112\); divide by 8: \(x = 14\)

Answer:

8