Question

question 3 not yet answered marked out of 2.00 flag question which are the correct measures for <wxz, <uzy, and <vyx? select one: a. <wxz = 152°, <uzy = 116°, and <vyx = 88° b. <wxz = 166°, <uzy = 106°, and <vyx = 92° c. <wxz = 162°, <uzy = 106°, and <vyx = 88° d. <wxz = 162°, <uzy = 106°, and <vyx = 92°

Explanation:

Step1: Find measure of $\angle WXZ$

$\angle WXZ$ and the $18^{\circ}$ angle are supplementary. So $\angle WXZ=180^{\circ}- 18^{\circ}=162^{\circ}$.

Step2: Find measure of $\angle UZY$

$\angle UZY$ and the $74^{\circ}$ angle are supplementary. So $\angle UZY = 180^{\circ}-74^{\circ}=106^{\circ}$.

Step3: Find measure of $\angle VYX$

In the triangle formed by $X$, $Y$ and the intersection on the line $WZ$, we know two - angles of the triangle. The third - angle (which is vertical to $\angle VYX$) can be found using the angle - sum property of a triangle. The two known angles in the triangle are $18^{\circ}$ and $74^{\circ}$. The third angle in the triangle is $180^{\circ}-(18^{\circ}+74^{\circ}) = 88^{\circ}$. Since vertical angles are equal, $\angle VYX=88^{\circ}$.

Answer:

C. $\angle WXZ = 162^{\circ},\angle UZY = 106^{\circ},\angle VYX = 88^{\circ}$