Answer:
m∠a = 100°
m∠b = 105°
m∠c = 25°
Explanation:
The line intersecting the triangle is parallel to the base of the triangle.
The intersecting line has created an additional smaller triangle (to the right of the diagram) which is similar to the larger triangle.
Therefore, the interior angles of the base of the smaller triangle are the same as the interior angles of the base of the original, larger triangle.
So the supplementary angle adjacent to ∠a will be 80°.
Similarly, the supplementary angle adjacent to ∠b will be 75°.
The sum of angles on a straight line is 180°
Therefore, m∠a = 180 - 80 = 100°
and, m∠b = 180 - 75 = 105°
The sum of interior angles of a triangle = 180°
Therefore, to determine m∠c, simply subtract 80° and 75° from 180°:
⇒ m∠c = 180 - 80 - 75 = 25°