Chapter 8.4, Problem 50STP

To determine

To calculate the value of $w+x+y+z$

Answer to Problem 50STP

The value of $w+x+y+z$ is ${280}^{\circ }$ . The correct answer is option B.

Explanation of Solution

Given information:

Consider the diagram given in the question.

The given options are,

A.140

B.280

C.320

D.360

From the diagram it is seen that $w\text{ and }x$ are two of three angles in a triangle and the third one is ${40}^{\circ }$ . It is known that perimeter of a triangle is ${180}^{\circ }$ , so can be written as,

  $\begin{array}{l}w+x+{40}^{\circ }={180}^{\circ }\\ w+x={180}^{\circ }-{40}^{\circ }\\ w+x={140}^{\circ }\end{array}$

Similarly, $y+z={140}^{\circ }$

Now, combine all to get the value of $w+x+y+z$

  $\begin{array}{l}w+x+y+z={140}^{\circ }+{140}^{\circ }\\ w+x+y+z={280}^{\circ }\end{array}$

Therefore, the value of $w+x+y+z$ is ${280}^{\circ }$