Question

given the triangle shown below with exterior angles that measure x°, y°, and z° as shown, what is the sum of x,y,z?

Answer 1

Given:

There are given that the triangle with an interior angle.

Where,

The interior angles are :

$72^{\circ}\text{ and 57}^{\circ}$

Explanation:

To find the value of the addition of x, y, and z, first, we need to draw the reimage.

Then,

The new image is:

Now,

First, we need to find the value of the angle of c.

Then,

From the formula to find the angle c:

$\angle a+\angle b+\angle c=180^{\circ}$

Then,

Put the value of a and b into the above formula:

Then,

$\begin{gathered} \operatorname{\angle}a+\operatorname{\angle}b+\operatorname{\angle}c=180^{\operatorname{\circ}} \\ 72^{\circ}+57^{\circ}+\operatorname{\angle}c=180^{\operatorname{\circ}} \\ 129^{\circ}+\angle c=180^{\circ} \\ \angle c=180^{\circ}-129^{\circ} \\ \angle c=51^{\circ} \end{gathered}$

Now,

Find all exterior angles x, y, and z.

Then,

First, find the value for x:

$\begin{gathered} \angle x=\angle a+\angle c \\ \angle x=72+51 \\ \angle x=123 \end{gathered}$

Then,

For the values of y:

$\begin{gathered} \angle y=\angle b+\angle c \\ \angle y=57+51 \\ \angle y=108 \end{gathered}$

And,

For the value of z:

Then,

$\begin{gathered} \angle z=\angle a+\angle b \\ \angle z=72+57 \\ \angle z=129 \end{gathered}$

Now,

Add the values of x, y and x:

Then,

$\begin{gathered} x+y+z=123+108+129 \\ =360 \end{gathered}$

Final answer:

Hence, the correct option is D.