Question

How do i solve this?

Answer 1

Explanation:

Answer 2

Answer: the value of
`\( x \)` is 105°

Explanation:

Given that lines
`\( p \)` and
`\( q \)` are parallel and the line that intersects them is transversal, several angle properties come into play.

1. Alternate Interior Angles are congruent when two parallel lines are intersected by a transversal. This means:

- The angle measuring 75° (between line p and the transversal) will be congruent to the angle opposite to it on the other side of the transversal but inside the parallel lines. This angle is adjacent to angle x, on line q.

2. Angles on a Straight Line add up to 180°. This means:

- If you know one of the angles, you can find the other by subtracting the known angle from 180°.

Using these properties:

Step 1: Using the Alternate Interior Angles property, the angle adjacent to angle x (on line q) is 75°.

Step 2: The angle x and this 75° angle are on a straight line (they are supplementary). Thus, they should add up to 180°.

Using the formula for angles on a straight line:

x + 75° = 180°

=> x = 180° - 75°

=> x = 105°

So, the value of
`\( x \)` is 105°.