The degree measure of the four angles of a quadrilateral are w,x,y,and z respectively. If w is the average (arithemetic mean) of x,y,z, then x + y + z = ? Is it 90 degrees?
x+y+z+w=360
x+y+z+ (x+y+z)/2=360
3(x+y+z)=720
x+y+z=720/3
check that
240 degrees?
It's not on the multiple choice list.
It's either
180 or 270 or 120 degrees.
(45 at least)
I think Bob has a typo in dividing x+y+z by 2 instead of 3
x+y+z+ (x+y+z)/3=360
3x+3y+3z + x+y+z = 1080
4x+4y+4z = 1080
x+y+z = 270
Thanks!
270 degrees is right.
Thought it was 180 .-.
To solve this problem, we need to use the given information that w is the average of x, y, and z, and then find the value of x + y + z.
Let's start by setting up an equation using the average value:
w = (x + y + z) / 3
To find x + y + z, we can multiply both sides of the equation by 3:
3w = x + y + z
Now, we know that the sum of all angles in a quadrilateral is always 360 degrees. Therefore, the sum of the four angles, w + x + y + z, should equal 360.
Thus, we have the equation:
w + x + y + z = 360
Since we want to find x + y + z, we can substitute 3w for w in the equation:
3w + x + y + z = 360
Rearranging this equation, we get:
x + y + z = 360 - 3w
So, x + y + z equals 360 minus three times the average angle (w), not necessarily 90 degrees.
To find the value of x + y + z, you need to know the specific value of w.