∠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?

Step-by-step explanation:

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

   ...(1)

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

    ...(2)

From (1) and (2), we get

Substitute and in the above equation.

Divide both sides by 8.

The value of y is 25.

Using equation (2), we get

Substitute y=25.

Therefore, .

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°