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Tamiku [17]
3 years ago
10

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

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
8 0

(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.

<em>Sum of the adjacent angles in a straight line = 180°</em>

⇒ m∠a + 80° = 180°

⇒ m∠a = 180° – 80°

⇒ m∠a = 100°

∠c and ∠a are vertically opposite angles.

<em>If two lines are intersecting, then the vertically opposite angles are congruent.</em>

⇒ ∠c ≅ ∠a

⇒ m∠c = m∠a

⇒ m∠c = 100°

<em>If two parallel lines are cut by a transversal, then the corresponding angles in the same side of the transversal are congruent.</em>

80° and angle b are corresponding angles.

⇒ m∠b = 80°

Hence m∠a = 100°, m∠b = 80° and m∠c = 100°.

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