Question

Please help! • all numbered streets runs parallel to each other. both 3rd and 4th streets are intersected by King Ave. as shown

Answer 1

(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°.