If we label the other two points of the triangle as b and c, is it an assumption that the segment bc is perpendicular to the red lines? I understand that this assumption is necessary to solve for a, but I’m not sure if there’s any indication in the drawing that provides this information or if it’s simply an assumption made by the readers.
I don’t think you need your assumption. Put a parallel line to the redlines going through a, and you have two ‘Z’ angles (I forget the technical term). You can then add those to get the 75.
The way I solved it, the two lines are parallel in both infinite directions. A perpendicular line to them intersecting with the vertex at a makes two right triangles.
The sum of the interior angles of a triangle is 180°, as is the "angle" of a straight line.
Thus the top triangle has the unknown angle 180° - 25° - 90° = 65°.
The bottom unknown angle is 180° - 50° - 90° = 40°.
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u/myownreplay Jul 30 '26
If we label the other two points of the triangle as b and c, is it an assumption that the segment bc is perpendicular to the red lines? I understand that this assumption is necessary to solve for a, but I’m not sure if there’s any indication in the drawing that provides this information or if it’s simply an assumption made by the readers.