The first observation we make is that the two triangles have two parallel sides. If we highlight relevant parts of the figure, we can make out a transversal that cuts two parallel lines.
According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the pair of alternate interior angles are congruent. Therefore, we can say that
x^(∘)=43^(∘).
To find y^(∘) we can use the Exterior Angle Theorem. The theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. We get the following equation.
43^(∘)+y^(∘)=75^(∘)
Let's solve this equation.
