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Wewaii [24]
3 years ago
9

Determine the measure of each angle using the picture below. Assume the two lines are parallel.

Mathematics
1 answer:
marta [7]3 years ago
8 0

Answer:

Step-by-step explanation:

Angle 5 is opposite to 37 => It's equal to 37.
Angle 6 and 7 are supplementary to angle 5 => They are equal to 180 - 37 = 143 each.

Angle 4 is corresponding to Angle 7, and since the 2 lines are parallel, it's equal to 143.

Angle 1 and 3 is supplementary to Angle 4, so they are equal to 180-143 = 37 each

Angle 2 is opposite to Angle 4, so it's equal to 143.


Answer : Angle 1,3,5 = 37
Angle 2,4,6,7 = 143

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Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
EastWind [94]

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The Law of Sines applies to any triangle and works as follows:

a/sinA = b/sinB = c/sinC

We are attempting to solve for every angle and every side of the triangle. With the given information, A = 61°, a = 17, b = 19, we can solve for the unknown angle that is B.

a/sinA = b/sinB

17/sin61 = 19/sinB

sinB = (19/17)(sin61)

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sin-1(sinB) = sin-1(0.9774)

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With angle B we can solve for angle C and then side c.

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The first solved triangle is:

A = 61°, a = 17, B = 77.8°, b = 19, C = 41.2°, c = 12.8

However, when we solved for angle B initially, that was not the only possible answer because of the fact that sinB = sin(180-B).

The other angle is simply 180°-77.8° = 102.2°. Therefore, angle B can also be 102.2° which will give us different values for c and C.

C = 180° - A - B

C = 180° - 61° - 102.2°

C = 16.8°

a/sinA = c/sinC

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The complete second triangle has the following dimensions:

A = 61°, a = 17, B = 102.2°, b = 19, C = 16.8°, c = 5.6

The answer you are looking for is the first option given in the question:

B = 77.8°, C = 41.2°, c = 12.8; B = 102.2°, C = 16.8°, c = 5.6

Step-by-step explanation:

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