Question

NO LINKS!!! Explain your answer in each case using if-then statements.

Answer 1

a) m∠? = 48°

If a transversal line intersects two parallel lines, then the resulting alternate interior angles are congruent.

b) m∠? = 71°

If a transversal line intersects two parallel lines, then the resulting corresponding angles are congruent.

c) m∠1 = 115°

If a transversal line intersects two parallel lines, then the resulting alternate exterior angles are congruent.

d) m∠2 = 62°

If a transversal line intersects two parallel lines, then the resulting same-side exterior angles are supplementary.

Explanation:

Part a

Alternate Interior Angles Theorem

If a transversal line intersects two parallel lines, then the angles that are interior to the parallel lines and on the opposite side of the transversal line are congruent.

If a transversal line intersects two parallel lines, then the resulting alternate interior angles are congruent.

`\implies m\angle ?=48^(\circ)`

Part b

Corresponding Angles Postulate

If a transversal line intersects two parallel lines, then the angles that are corresponding (in the matching corners) are supplementary.

If a transversal line intersects two parallel lines, then the resulting corresponding angles are congruent.

`\implies m\angle ?=71^(\circ)`

Part c

Alternate Exterior Angles Theorem

If a transversal line intersects two parallel lines, then the angles that are exterior to the parallel lines and on the opposite side of the transversal line are congruent.

If a transversal line intersects two parallel lines, then the resulting alternate exterior angles are congruent.

`\implies m\angle 1=115^(\circ)`

Part d

Same-side Interior Angles Theorem

If a transversal line intersects two parallel lines, then the angles that are interior to the parallel lines and on the same side of the transversal line are supplementary.

If a transversal line intersects two parallel lines, then the resulting same-side exterior angles are supplementary.

`\implies m\angle 2+118^(\circ)=180^(\circ)`

`\implies m\angle 2=62^(\circ)`