Given:
The lines l and m are parallel to each other.
The measure of angles are given as,
[tex]\begin{gathered} m\angle1=(3x+16)\degree \\ m\angle2=(x+12)\degree \end{gathered}[/tex]
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.
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.
[tex]m\angle1+m\angle2=180\degree\text{ . .. . (1)}[/tex]
b)
To find x:
On plugging the given values in equation (1),
[tex](3x+16)+(x+12)=180\degree[/tex]
On further solving the above equation,
[tex]\begin{gathered} 4x+28=180 \\ 4x=180-28 \\ x=\frac{152}{4} \\ x=38 \end{gathered}[/tex]
Thus, the value of x is 38.
c)
To find m∠1 and m∠2:
Substitute the value of x in the given expressions.
[tex]\begin{gathered} m\angle1=3(38)+16=130 \\ m\angle2=38+12=50 \end{gathered}[/tex]
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°.
