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MariettaO [177]
3 years ago
12

What is the measure of

Mathematics
1 answer:
Ede4ka [16]3 years ago
5 0

Hey there! :)

Answer:

m∠A = 72°.

m<B = 108°.

Step-by-step explanation:

In a parallelogram, the opposite angles are congruent.

Therefore, we can set the two expressions equal to each other:

5y - 3 = 3y + 27

Add 3 to both sides:

5y = 3y + 30

Subtract 3y from both sides:

2y = 30

Divide both sides by 2:

y = 15

Substitute this value of y into an expression to solve for the measure of ∠A:

5(15) - 3 = 72°. m∠A = 72°.

In parallelograms, the neighboring angles are supplementary. Therefore:

m∠A + m∠B = 180°

72° + m∠B = 180°

m<B = 108°.

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Zina [86]

Question:

If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___  and tan(θ) =___.

Answer:

Sin\theta = \frac{-15}{17}

Tan\theta = \frac{15}{8}

Step-by-step explanation:

Given

cos(θ) =-8/17

Required

sin(θ) = __

tan(θ) =__

The first step is to determine the length of the third side

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cos(\theta) = \frac{Adj}{Hyp}

Where Adj and Hyp represent Adjacent and Hypotenuse

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The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such

Opp = -15

From trigonometry

Sin\theta = \frac{Opp}{Hyp}

Sin\theta = \frac{-15}{17}

Also from trigonometry

Tan\theta = Sin\theta / Cos\theta

Tan\theta = \frac{-15}{17} / \frac{-8}{17}

Tan\theta = \frac{-15}{17} * \frac{-17}{8}

Tan\theta = \frac{-15 * -17}{17  * 8}

Tan\theta = \frac{15 * 17}{17  * 8}

Tan\theta = \frac{15}{8}

5 0
3 years ago
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