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8090 [49]
2 years ago
7

Find the measure of the indicated angle. Round to the nearest tenth.

Mathematics
1 answer:
erik [133]2 years ago
4 0

Answer:

Step-by-step explanation:

cos θ=12/16=3/4=0.75

θ=cos^{-1}(0.75)≈41.4°

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The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

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∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

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Subtract 72° from both sides.

m∠DAE = 108°

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⇒ m∠CAF = m∠DAE

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m∠CAB + m∠BAF = 108°

m∠BAF + m∠BAF = 108°

2 m∠BAF = 108°

Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

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3 years ago
Jim decides to start a small nonprofit business of renting out motor scooters to help out his area residents. He puts in his own
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First, find the expected number of scooters rented per month:

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