Answer:
x=20
Step-by-step explanation:
Hi there!
We are given 2 intersecting lines, and the values of 2 angles
One of the angles is 120°, while the other is 6x
We want to find the value of x
There are many ways to approach this problem, but here is one way:
The angle adjacent to the 120° angle (the angle to the right of it), plus the 120 degree angle equals 180° (because the horizontal line is a straight line, meaning it makes a straight angle, which is 180 degrees. The reason why we can add the 2 angles together and it equals 180 is due to a postulate, called the Angle Addition Postulate).
Let's call the value of this unknown angle y (we don't know that it is the same value as x)
so 120 + y = 180
Subtract 120 from both sides
y=60
So the measure of the angle adjacent to the 120° angle is 60°
Now, the vertical line is also a straight angle, and the 60 degree angle we just found + 6x = 180
As an equation, this would mean:
60 + 6x = 180
Subtract 60 from both sides
6x=120
Divide both sides by 6
x=20
Hope this helps!
Please see the picture for a visual.
