(a) m∠a = 100°
(b) m∠b = 80°
(c) m∠c = 100°
Solution:
Given 3rd and 4th street are parallel lines and King Ave is a transveral line.
Sum of the adjacent angles in a straight line = 180°
⇒ m∠a + 80° = 180°
⇒ m∠a = 180° – 80°
⇒ m∠a = 100°
∠c and ∠a are vertically opposite angles.
If two lines are intersecting, then the vertically opposite angles are congruent.
⇒ ∠c ≅ ∠a
⇒ m∠c = m∠a
⇒ m∠c = 100°
If two parallel lines are cut by a transversal, then the corresponding angles in the same side of the transversal are congruent.
80° and angle b are corresponding angles.
⇒ m∠b = 80°
Hence m∠a = 100°, m∠b = 80° and m∠c = 100°.