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Taya2010 [7]
3 years ago
9

Two angles are complementary. The measure of one angle is 6º more than five times the measure of the other angle. Find the

Mathematics
2 answers:
Nina [5.8K]3 years ago
8 0
14 degrees and 76 degrees
Salsk061 [2.6K]3 years ago
6 0

Complementary means that the two angles sum to 90 degrees.

So based on the problem, let:

1st angle=5x+6

2nd angle=x

Now create an equation.

x+5x+6=90

6x=84

x=14

5x+6=76

answer: 14 degrees and 76 degrees

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Answer:

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Step-by-step explanation:

Side 'a' is the shortest of three unequal sides, so angle A will be the smallest angle in the triangle. Its measure can be found from the Law of Cosines.

  a² = b² +c² -2bc·cos(A)

  cos(A) = (b² +c² -a²)/(2bc) = (21² +25² -17²)/(2·21·25) = 777/1050

  A = arccos(777/1050) ≈ 42.3°

The measure of angle A is about 42.3°.

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<u><em>Additional comment</em></u>

The smallest angle in a triangle can never be greater than 60°. This lets you eliminate choices that exceed that value.

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