Question

Could someone help me with one question?

Answer 1

Let's start by just looking at y and the 116-deg angle, ok?

Answer 2

Ok.

Answer 3

See figure below.
The angles with measures a and b are called a "linear pair." They are formed by a straight line and one ray. Angles of a linear pair are supplementary. That means their measures add up to 180 deg.

Answer 4

Now look in your problem an the angles measuring y and 116 deg.
Notice that they are a linear pair.
What does that tell you about the sum of their measures?

Answer 5

That it will be the same measure?

Answer 6

It means the sum of their measures is 180 degrees.
That means you can write this equation to find the measure of y:
y + 116 = 180
Now solve the equation for by by subtracting 116 from both sides.
What do you get for y?

Answer 7

64, sorry my computer crashed.

Answer 8

Sorry, so did mine.

Answer 9

You are correct. y = 64.

Now we need x.
x and y are angles in a quadrilateral. A quadrilateral is a polygon with 4 sides.

There is a formula that let's you find the sum of the measures of the angles of a polynomial. It is:
\( 180( n - 2) \)
where n = number of sides.

Since we have a polygon with 4 sides, the sum of the measures of its angles is
\( 180(4 - 2) = 180(2) = 360\)

Answer 10

You know that the sum of the measures of the 4 angles is 360, and only one angle is unknown , so you can solve for it.

\( x + 64 + 72 + 125 = 360\)

Solve the equation for x.