Answer:
x = 30°, y = 80°
x = 40°, y = 50°
Explanation:
Alternate Interior Angles Theorem
If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.
Therefore, as the two horizontal lines are parallel:
⇒ x = 30°
Exterior Angle Theorem
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ y = 50° + x°
⇒ y = 50° + 30°
⇒ y = 80°
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Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore, the angles marked red on the attached diagram are equal.
This means that the two triangles outlined in green are similar.
If two triangles are similar, their corresponding angles are congruent.
⇒ x = 40°.
Interior Angles of a Triangle
The interior angles of a triangle sum to 180°.
Therefore:
⇒ 90° + x + y = 180°
⇒ 90° + 40° + y = 180°
⇒ 130° + y = 180°
⇒ y = 50°