Question

In $\Delta ABC$, what is the value of $w+x+y+z$?

Short answer

The value of $w+x+y+z$ is $240°$.

Step-by-step solution

Step-1 – Apply the concept of angle sum property of triangle

Sum of all angles of a triangle is always $180°$.

Step-2 –Find the values of angles

Consider the provided$\Delta ABC$

Apply the angle sum property in smaller triangle.

$\begin{array}{c}60°+w°+x°=180°\\ w°+x°=180°-60°\\ w°+x°=120°\end{array}$

Let $w{}^{\circ }+x{}^{\circ }=120°$ …(1)

Apply the angle sum property in big triangle.

$\begin{array}{c}60°+y°+z°=180°\\ y°+z°=180°-60°\\ y°+z°=120°\end{array}$

Let $y{}^{\circ }+z{}^{\circ }=120°$ …(2)

Step-3 –Calculation step

The objective is to find the value of $w{}^{\circ }+x{}^{\circ }+y{}^{\circ }+z°$.

Add the equations (1) and (2).

$\begin{array}{c}w°+x°+y°+z°=120°+120°\\ w°+x°+y°+z°=240°\end{array}$

Thus, the value of $w+x+y+z$ is $240°$.