A pair of parallel lines is cut by a transversal. What are the measures of the two marked angles?
CHOICES

40 degrees and 40 degrees

40 degrees and 140 degrees

65 degrees and 115 degrees

75 degrees and 105 degrees

Answer:

Let us mark the points R and S on line p, T and U on line q, A and B on line l and C and D on line m.

Suppose the lines p and q intersect the line l at K and L respectively and line m at N and M respectively.

Since, AB is a straight line and ray KN stands on it, then

∠NKL + ∠NKA = 180∘ (Angles in a linear pair)

⇒110∘ + a = 180∘

⇒a = 180∘ − 110∘ = 70∘

Since, line p || line q and line l is a transversal intersecting them at K and L, then

∠TLB = ∠NKA (Alternate exterior angles)

⇒b = a

⇒b = 70∘

Since, line p || line q and line m is a transversal intersecting them at N and M, then

∠CNK = ∠NML (Corresponding angles)

⇒c = 115∘

Since, CD is a straight line and ray ML stands on it, then

∠NML + ∠LMD = 180∘ (Angles in a linear pair)

⇒115∘ + d = 180∘

⇒d = 180∘ − 115∘ = 65∘

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I WILL MARK BRAINEST IF YOU ANSWER CORRECTLY Which shows the correct way to use the rule “multiply by the reciprocal” for the expression below? 5 divided by StartFraction 2 Over 9 EndFraction StartFraction 5 Over 1 EndFraction times StartFraction 9 Over 2 EndFraction = StartFraction 45 Over 2 EndFraction StartFraction 5 Over 1 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 10 Over 9 EndFraction StartFraction 1 Over 5 EndFraction times StartFraction 9 Over 2 EndFraction = StartFraction 9 Over 10 EndFraction StartFraction 1 Over 5 EndFraction times StartFraction 2 Over 9 EndFraction = StartFraction 2 Over 45 EndFraction

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