Question

1. a new water slide is being created at a local waterpark. a basic blueprint has been drawn. what are the missing interior angles? select two correct answers. a. the m∠x is 119°. b. the m∠y is 61°. c. the m∠z is 153°. d. the m∠x is 34°. e. the m∠y is 27°.

Explanation:

Step1: Find angle x

Use the property that a straight - line angle is 180°. Angle x and the 153° angle are supplementary. So, $x = 180 - 153$.
$x=27^{\circ}$

Step2: Find angle y

Use the property that the sum of angles in a triangle is 180°. In the triangle with angles 61°, z, and y, first find angle z. Angle z and the 153° angle are linear - pair, so $z = 180 - 153=27^{\circ}$. Then, $y=180-(61 + 27)$.
$y = 92^{\circ}$

Step3: Check the options

We found $x = 27^{\circ}$ and $z = 27^{\circ}$.

Answer:

D. The $m\angle x$ is 27°.
E. The $m\angle y$ is 27°. (There is a mistake in the problem - statement options as we calculated $y = 92^{\circ}$, but based on the correct calculation of $x$ the correct answer for $x$ value is D)