Problem Analysis:
The image shows a geometric figure with parallel lines and a transversal. The goal is to determine the value of the angle \( x \). Let's break down the problem step by step.
#### Key Observations:
1. The two horizontal lines are marked as parallel.
2. There is a transversal intersecting these parallel lines.
3. One of the angles formed by the transversal is given as \( 124^\circ \).
4. There is a right angle (marked with a red square) in the figure.
5. We need to find the value of the angle \( x \).
#### Step-by-Step Solution:
##### Step 1: Identify the relationship between the given angle and the parallel lines.
The angle \( 124^\circ \) is an exterior angle formed by the transversal and one of the parallel lines. Since the lines are parallel, the corresponding interior angle on the same side of the transversal will be supplementary to \( 124^\circ \). This means:
\[
\text{Interior angle} = 180^\circ - 124^\circ = 56^\circ
\]
##### Step 2: Use the right angle to find the value of \( x \).
The right angle (90°) is part of a triangle formed by the transversal and the parallel lines. In this triangle, the sum of the angles must be \( 180^\circ \). The triangle has:
- One angle of \( 90^\circ \) (the right angle),
- One angle of \( 56^\circ \) (the interior angle we calculated),
- The third angle, which is \( x \).
Using the angle sum property of a triangle:
\[
90^\circ + 56^\circ + x = 180^\circ
\]
##### Step 3: Solve for \( x \).
\[
90^\circ + 56^\circ + x = 180^\circ
\]
\[
146^\circ + x = 180^\circ
\]
\[
x = 180^\circ - 146^\circ
\]
\[
x = 34^\circ
\]
Final Answer:
\[
\boxed{34^\circ}
\]
Thus, the correct option is \(\boxed{B}\).
Parent Tip: Review the logic above to help your child master the concept of equilateral and isosceles triangles worksheet.
