The measure of angle a, b, c, d are 108°, 53°, 53°, 19° respectively.
Angle a = 108° (exterior angle)
Angle c = 53° (alternate interior angle)
Here's how to solve for angle d:
Identify congruent angles: Since we have parallel lines cut by a transversal, we know that:
Angle b = Angle c = 53° (alternate interior angles)
Use the angle sum property of a triangle: In triangle abc, the angles must add up to 180°. Therefore:
Angle a + Angle b + Angle c = 180°
Substitute the known values:
108° + 53° + Angle d = 180°
Solve for angle d: Combine like terms:
161° + Angle d = 180°
Subtract 161° from both sides:
Angle d = 180° - 161°
Therefore, Angle d = 19°.