Question

Find x if the angles of a quadrilateral are 2x, 3x, 4x, and 5x

Answer 1

x= 25.71 or 25º 42' 36''

Explanation:

To solve this we need to remember the theorem about the angles of a quadrilateral which says that "The sum of the interior angles of any quadrilateral is 360º"

In this problem we have that the angles are 2x, 3x, 4x and 5x. So now we know that these four angles have to sum up 360.

We are going to write the equation representing this and we will solve for x:

`2x +3x+4x+5x = 360\\14x=360\\x=360/14\\x= 25.71`

Therefore, x = 25.71

If you want, you can transform this x into its degrees minutes seconds expression:

To do this, you take the decimal part of the number you got and multiply for 60 to get the minutes:

.71 x (60) = 42.6 This means that we have 42 minutes.

Now we're going to take the remaining decimal part on the last answer and multiply for .60 to get the seconds.

.6 x (60) = 36 This means that we have 36 seconds.

Therefore, x = 25.71 or 25º 42' 36''

Answer 2

To solve this we are going to take advantage of the fact the the sum of the interior angles of a quadrilateral is always 360°. So, we can add up all our angles and set them equal to 360°:

`2x+3x+4x+5x=360`
Now, we just need to solve for
`x`:

`2x+3x+4x+5x=360`

`14x=360`

`x= (360)/(14)`

`x= (180)/(7)`

We can conclude that the value of
`x` in our quadrilateral is
`(180)/(7)`°, or we can conclude that
`x` is approximately 25.7° (in decimal form).