Answer:
[tex]x=34[/tex]
Step-by-step explanation:
The angle that is 4x is a vertical angle to 3x plus the mystery angle
So we can make an equation for that to find the mysterious angle
?+3x=4x
Subtract both sides by 3x
[tex]?=x[/tex]
So the mystery angle in the smaller triangle is x so to find the other angle in that triangle we see it is next to the angle 68 and since they are both on a straight line we can subtract 68 from 180 to find that angle
[tex]180-68=112[/tex]
Now we know the all three angles in the smaller triangle is
112
x
x
The sum of all three angles in any triangle equals 180 so we can make an equation to find x
[tex]112+x+x=180[/tex]
Simplify
[tex]112+2x=180[/tex]
Subtract both sides by 112
[tex]2x=68[/tex]
Divide both sides by 2
[tex]x=34[/tex]
I hope this helps
