Question

NO LINKS!! Explain your reasoning using if-then statements Part 2

Answer 1

a) x = 11

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

b) x = 7

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

Explanation:

Part a

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 (4x+1)^(\circ)=45^(\circ)`

`\implies 4x+1=45`

`\implies 4x=44`

`\implies x=11`

Part b

Same-side Exterior Angles Theorem

If a transversal line intersects two parallel lines, then the angles that are exterior 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 (9x+2)^(\circ)+(17x-4)^(\circ)=180^(\circ)`

`\implies 9x+2+17x-4=180`

`\implies 9x+17x+2-4=180`

`\implies 26x-2=180`

`\implies 26x=182`

`\implies x=7`