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∠1and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠1=(3y+10)∘ and m∠3=(5y−30)∘. What is m∠2?

kykrilka [37]

Answer:

$m\angle 2=95^{\circ}$

Step-by-step explanation:

It is given that ∠1 and ∠2 are a linear pair. So, there sum is 180 degrees.

$m\angle 1+m\angle 2=180^{\circ}$ ...(1)

∠2 and ∠3 are vertical angles. So, both are equal.

$m\angle 2=m\angle 3$ ...(2)

From (1) and (2), we get

$m\angle 1+m\angle 3=180^{\circ}$

Substitute $m\angle 1=(3y+10)^{\circ}$ and $m\angle 3=(5y-30)^{\circ}$ in the above equation.

$(3y+10)^{\circ}+(5y-30)^{\circ}=180^{\circ}$

$(8y-20)^{\circ}=180^{\circ}$

$8y-20=180$

$8y=180+20$

Divide both sides by 8.

$y=\dfrac{200}{8}$

$y=25$

The value of y is 25.

Using equation (2), we get

$m\angle 2=m\angle 3=(5y-30)^{\circ}$

Substitute y=25.

$m\angle 2=(5(25)-30)^{\circ}$

$m\angle 2=(125-30)^{\circ}$

$m\angle 2=95^{\circ}$

Therefore, $m\angle 2=95^{\circ}$ .

6 0

3 years ago

The probability that she will toss tails and a number less than 3

alexandr402 [8]

The probability of getting tails on a coin is 0.5 or 1/2.
The probability of getting a number LESS than 3 on a dice is 2/6 or 1/3.
Why? Because less than 3 means {1, 2} are counted but {3, 4, 5, 6} are not in the probability. So it's 2/6 with 6 sides on a dice.

To find the probability of both occurring at once, multiply the two probabilities together, 1/2 * 1/3, and you will get 1/6.

The answer therefore is 1/6 (A).

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6 0

3 years ago

What the square root of 20?

Arada [10]

Answer:

4.472135955

Step-by-step explanation:

The square root is 4.472135955

Rounded to one decimal place= 4.5