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655-705 (Hard)|   Geometry|      
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Bunuel
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Newtown is due north of Oscarville. Highway L runs 31° south of east 05 Feb 2018, 06:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

53% (02:22) correct 47% (01:49) wrong based on 64 sessions

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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°
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C
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Newtown is due north of Oscarville. Highway L runs 31° south of east 05 Feb 2018, 08:14
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Bunuel
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°
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This is how i attempted it
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File comment: Hope this is right
IMG_20180205_203843[1].jpg
IMG_20180205_203843[1].jpg [ 3.37 MiB | Viewed 2258 times ]

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Newtown is due north of Oscarville. Highway L runs 31° south of east 06 Feb 2018, 18:06
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Bunuel
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°
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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.



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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