Parallel Lines Geometry: Calculate Angle α Using 62° and 54° Measurements

Please note that according to the definition of corresponding angles, the angle $\alpha$corresponds to the angle located on line a and is also within the small triangle created in the drawing.

As we already have one angle in this triangle, we will try to find and calculate the remaining angles.

Furthermore the angle opposite to the angle 62 next to the vertex is also equal to 62 (vertex opposite angles are equal to one other)

Therefore, we can now calculate the missing angle in the small triangle created in the drawing, which is the angle

$\alpha$

$\alpha=180-54-62$

$\alpha=64$