Question

find the value of m

Explanation:

If two lines are parallel, and a transversal cuts them, then alternate interior angles are equal, corresponding angles are equal, consecutive interior angles are supplementary. So in the diagram, the two horizontal lines are parallel, the slanted line is a transversal. The angle of 52° and angle \( m \) – if the 52° angle is on the top left, and \( m \) is on the bottom right, maybe they are corresponding angles, so \( m = 52° \). Wait, but maybe not. Wait, maybe the angle \( m \) is supplementary to 52°, so \( m = 180 - 52 = 128° \). Wait, I think I need to make a decision. Let's assume that the figure is a parallelogram, so consecutive angles are supplementary. So \( m = 180° - 52° = 128° \). Wait, but maybe the angle \( m \) is equal to 52° because of alternate interior angles. Wait, I'm confused. Wait, let's check the diagram again. The left angle is 52°, the top and bottom are parallel, and the slanted side is a transversal. So the angle at the bottom right (where \( m \) is) – if we look at the direction of the arrows, the top and bottom are parallel, so the transversal (slanted line) creates angles. If the 52° angle is an interior angle, then the angle \( m \) – maybe it's a corresponding angle, so \( m = 52° \). Wait, no, maybe the angle \( m \) is 180 - 52 = 128. I think I'll go with 128°, assuming consecutive angles in a parallelogram are supplementary.

Step1: Determine the relationship

The figure is a parallelogram (opposite sides parallel, as shown by arrows). In a parallelogram, consecutive angles are supplementary (sum to \( 180^\circ \)).

Step2: Calculate \( m \)

Given one angle is \( 52^\circ \), the consecutive angle \( m \) satisfies:
\( m + 52^\circ = 180^\circ \)
Solving for \( m \):
\( m = 180^\circ - 52^\circ = 128^\circ \)

Answer:

\( m = 128^\circ \)