Question

The support for a window air conditioning unit forms a triangle and an exterior angle. What is the measure

Answer 1

You have to find first the value of x, which means that you have to add all the interior angles and have the equation equal to 180 like this:

3x+5x-6+90= 180 (remember that the form of the triangle is a right triangle, which means you have a 90 degree angle.)

The value of x is going to be equal to 12. (x=12)

Now, substitute in the given angles
3(12)= 36
5(12)-6= 54

You have to remember that exterior angles also sum up to 180 degrees, and since we already have the value of the exterior angle, 3x, now we are able to know the value of what they are asking you for, which is a simple subtraction 180-36= 144.

Hope it helps! :)

Answer 2

126°

Explanation:

We know that the sum of all internal angles of a triangle must sum 180, that is

`(5x-6)+3x+90=180\\8x=180-84\\x=(96)/(8)\\ x=12`

By sum of angle, we know that the exterior angle and the adjacent interior angle must sum 180, because they are on a straight angle

`y+5x-6=180`

But,
`x=12`

So,

`y+5(12)-6=180\\y+60-6=180\\y=180-54\\y=126\°`

Therefore, the exterior angle measures 126°.