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Airida [17]
3 years ago
7

∠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?

Mathematics
1 answer:
kykrilka [37]3 years ago
6 0

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}.

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