Answer:
∠6=116°
Step-by-step explanation:
Buckle up :)
- We are given the values of ∠4 [tex](-2x+94)[/tex] and ∠8 [tex](-5x+139)[/tex].
- Vertical angles are congruent. Angle 4 and angle 1 are vertical angles, so angle 1 is also [tex]-2x+94[/tex].
- ∠1 and ∠8 are alternate exterior angles. The transversal is the line that crosses over the parallel lines. When two angles are on opposite sides of the transversal, they are alternate angles. When the two angles are on the outside of the parallel lines, they are exterior angles. This makes them alternate-exterior angles.
- Alternate exterior angles are congruent. This means that ∠1≅∠8. Write an equation in order to solve for x:
[tex]-2x+94=-5x+139[/tex]
Solve for x. Subtract 94 from both sides:
[tex]-2x+94-94=-5x+139-94\\\\-2x=-5x+45[/tex]
Add 5x to both sides:
[tex]-2x+5x=-5x+5x+45\\\\3x=45[/tex]
Divide both sides by 3:
[tex]\frac{3x}{3} =\frac{45}{3} \\\\x=15[/tex]
Insert the value of x into angle 4 because they are same-side interior angles. This is because they are on the same side of the transversal and within the parallel lines. Same-side interior angles are supplementary, so their value will add up to 180°. Therefore, in order to find angle 6, we need to first find the true value of angle 4:
[tex]x=15\\\\-2(15)+94\\\\-30+94\\\\64[/tex]
∠4 is 64°. Use ∠a+∠b=180 to find angle 6:
[tex]a+64=180[/tex]
a represents angle 6. Subtract 64 from both sides:
[tex]a+64-64=180-64\\\\a=116[/tex]
Angle 6 has a measure of 116°.
:Done
