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Newtown is due north of Oscarville. Highway L runs 31° south of east

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Newtown is due north of Oscarville. Highway L runs 31° south of east [#permalink]

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New post 05 Feb 2018, 05:50
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Newtown is due north of Oscarville. Highway L runs 31° south of east from Newtown and Highway M runs 44° north of east from Oscarville. If L and M are straight, what is the measure of the acute angle they form at their intersection?

(A) 105°

(B) 89°

(C) 75°

(D) 59°

(E) 46°
[Reveal] Spoiler: OA

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Re: Newtown is due north of Oscarville. Highway L runs 31° south of east [#permalink]

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New post 05 Feb 2018, 07:14
Bunuel wrote:
Newtown is due north of Oscarville. Highway L runs 31° south of east from Newtown and Highway M runs 44° north of east from Oscarville. If L and M are straight, what is the measure of the acute angle they form at their intersection?

(A) 105°

(B) 89°

(C) 75°

(D) 59°

(E) 46°


This is how i attempted it
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Re: Newtown is due north of Oscarville. Highway L runs 31° south of east [#permalink]

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New post 06 Feb 2018, 17:06
Bunuel wrote:
Newtown is due north of Oscarville. Highway L runs 31° south of east from Newtown and Highway M runs 44° north of east from Oscarville. If L and M are straight, what is the measure of the acute angle they form at their intersection?

(A) 105°

(B) 89°

(C) 75°

(D) 59°

(E) 46°


We see that Newtown, Oscarville, and the intersection of Highways L and M form a triangle. Since Highway L makes an angle of 31 degrees south of east from Newtown, we see that angle a = 90 - 31 = 59 degrees. Similarly, since Highway M makes an angle of 44 degrees north of east of Oscarville, we see that angle b = 90 - 44 = 46 degrees.

Image

Thus, we see that angle x, the acute angle between the two highways, is 180 - a - b = 180 - 59 - 46 = 75 degrees.

Answer: C
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Re: Newtown is due north of Oscarville. Highway L runs 31° south of east   [#permalink] 06 Feb 2018, 17:06
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Newtown is due north of Oscarville. Highway L runs 31° south of east

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