Question

Triangle XYZ has vertices X(–1, –1), Y(–2, 1), and Z(1, 2). What is the approximate measure of angle Z?

Answer 1

The answer to this question is A. 37.2°

Answer 2

Answer:

37.9°

Step-by-step explanation:

Notice that angle Z is formed by sides XZ and YZ.

First, we need to find the slopes of each side.

$m_{XZ}=\frac{2-(-1)}{1-(-1)}= \frac{2+1}{1+1}=\frac{3}{2}$

The slope of side XZ is 3/2.

$m_{YZ}=\frac{2-1}{1-(-2)}=\frac{1}{1+2}=\frac{1}{3}$

The slope of side YX is 1/3.

Now, we need to recur to the angle-slope formula, which is gonna give us the angle between both sides, that is, angle Z.

$tan(\angle Z)=|\frac{m_{XZ}-m_{YZ}}{1+(m_{XZ})(m_{YZ})} |$

Replacing each slope, we have

$tan(\angle Z)=|\frac{\frac{3}{2}-\frac{1}{3} }{1+\frac{3}{2}(\frac{1}{3})} |\\tan(\angle Z)=|\frac{\frac{9-2}{6} }{1+\frac{1}{2} } |=|\frac{\frac{7}{6} }{\frac{3}{2} } |\\tan(\angle Z)=|\frac{14}{18} |=|\frac{7}{9} |$

Then, we solve for $\angle Z$

$\angle Z=tan^{-1}(\frac{7}{9} ) \approx 37.9\°$

Therefore, the approximate measure of angle Z is 37.9°