Question

Solve for x to make A||B

Answer 1

To make lines A||B, the value of x should be approximately 11.43 degrees.

Here's the solution:

- Lines A and B: The image shows two lines, A and B, intersected by a transversal.

- Angle Measures: The transversal forms several angles, with measures of 80 degrees, 7x degrees, 50 degrees, and a straight angle.

Key Property:

Alternate Interior Angles: When a transversal intersects parallel lines, the alternate interior angles are equal.

Solution Steps:

1. Identify Alternate Interior Angles: In the image, the angles measuring 80 degrees and 7x degrees are alternate interior angles.

2. Set Angles Equal: To make A||B, these angles must be equal. Therefore, we set up the equation:

80 = 7x

3. Solve for x: Dividing both sides by 7, we get:

x = 80/7

x ≈ 11.43 degrees

To make lines A||B, the value of x should be approximately 11.43 degrees.

Answer 2

Answer: x = 50

Explanation:

In the given image, the alternate interior angles are equal. Therefore, 80 + x = 180 - 50 (since straight angles measure 180 degrees). Simplifying this equation, we get 130 + x = 180, which gives us x = 50 degrees. Thus, A||B when x = 50 degrees.