Question

The degree measures of the four angles of a quadrilateral are w,x, y, and z respectively. If w is the average (arithmetic mean) of x, y, and z, then x + y + z =A. 45 degreesB. 90 degreesC.120°D.270⁰

Answer 1

It is stated that the sum of the interior angles of a quadrilateral is 360°. It means that:

`w+x+y+z=360`

If w is the average of x, y and z, then:

`w=(x+y+z)/(3)`

Use this information to replace w in the first equation:

`\begin{gathered} (x+y+z)/(3)+x+y+z=360 \\ (4)/(3)(x+y+z)=360 \\ x+y+z=360\cdot(3)/(4) \\ x+y+z=270 \end{gathered}`

x+y+z=270°.