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:

$w=\frac{x+y+z}{3}$

Use this information to replace w in the first equation:

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

x+y+z=270°.