Answer:
x=15
Step-by-step explanation:
Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.
Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:
[tex](2x+10)+(4x+80)=180[/tex]
Solve for x. Remove the parentheses and combine like terms:
[tex]2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180[/tex]
Work to isolate the variable, x. Subtract 90 from both sides:
[tex]6x+90-90=180-90\\\\6x=90[/tex]
Isolate x. Divide both sides by 6:
[tex]\frac{6x}{6}=\frac{90}{6} \\\\x=15[/tex]
The value of x is 15.
:Done
If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:
[tex]2x+10\\\\2(15)+10\\\\30+10\\\\40[/tex]
∠2=40
[tex]4x+80\\\\4(15)+80\\\\60+80\\\\140[/tex]
∠4=140
∠2+∠4=180
40+140=180
The value of x is true.
