Answer:
The value of 'x' is 7 that will make make L║M.
Step-by-step explanation:
Given,
Line segment L and line segment M are cut by a transversal line.
We can name it as 't' transversal line and also the given angle measures as ∠1 and ∠2.
So, ∠1 = [tex]7x+9[/tex]
∠2 = [tex]8x+2[/tex]
We have to find the value of 'x'.
Solution,
Since L and M are two line segment which is cut by another line segment 't'.
For L║M, the measure of ∠1 and ∠2 must be equal according to corresponding angle property.
"When the measure of a pair of same side corresponding angle is equal, then the line segments are parallel".
[tex]\therefore \angle1=\angle2[/tex]
On substituting the values, we get;
[tex]7x+9=8x+2[/tex]
Combining the like terms, we get;
[tex]8x-7x=9-2\\\\x=7[/tex]
Now we will find out the measure of ∠1 and ∠2.
[tex]\angle1=7x+9=7\times7+9=49+9 =58[/tex]
[tex]\angle2=8x+2=8\times7+2=56+2=58[/tex]
Hence The value of 'x' is 7 that will make make L║M.
