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Hey i need help! and show your work

Hey i need help! and show your work-example-1

1 Answer

13 votes

Answer:

x=20

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.

Hey i need help! and show your work-example-1
User Aaron Lerch
by
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