Question

Part A: Which relationship describes <1 and <2? Part B: What is the value of x? Part C: What is the m<1 & m<2?

Answer 1

Given:

The lines l and m are parallel to each other.

The measure of angles are given as,

`\begin{gathered} m\angle1=(3x+16)\degree \\ m\angle2=(x+12)\degree \end{gathered}`

The objective is,

a) To describe the relation between ∠1 and ∠2.

b) To find the value of x.

c) To find the measure of m∠1 and m∠2.

Step-by-step explanation:

a)

To obtain relationship:

Since l and m are parallel lines then the angles on the same side of the transverse will be supplementary angles.

`m\angle1+m\angle2=180\degree\text{ . .. . (1)}`

b)

To find x:

On plugging the given values in equation (1),

`(3x+16)+(x+12)=180\degree`

On further solving the above equation,

`\begin{gathered} 4x+28=180 \\ 4x=180-28 \\ x=(152)/(4) \\ x=38 \end{gathered}`

Thus, the value of x is 38.

c)

To find m∠1 and m∠2:

Substitute the value of x in the given expressions.

`\begin{gathered} m\angle1=3(38)+16=130 \\ m\angle2=38+12=50 \end{gathered}`

Hence,

a) The angles ∠1 and ∠2 are supplementary angles.

b) The value of x is 38.

c) The measure of ∠1=130° and the measure of ∠2=50°.