Question

∠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?

Answer 1

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