Question

find the measure of the three missing angles in the rhombus below.
question
answer
attempt 1 out of 2
x =
y =
z =

Explanation:

Step1: Properties of a rhombus

In a rhombus, opposite angles are equal. So, $x = 113^{\circ}$ (since it is opposite to the $113^{\circ}$ angle).

Step2: Sum of adjacent angles

Also, adjacent angles in a rhombus are supplementary (sum to $180^{\circ}$). Let's find $y$.
We know that $y+113^{\circ}=180^{\circ}$.
So, $y = 180^{\circ}- 113^{\circ}=67^{\circ}$.

Step3: Opposite angles property again

Since $z$ is opposite to $y$, by the opposite - angles - equal property of a rhombus, $z = y = 67^{\circ}$.

Answer:

$x = 113$, $y = 67$, $z = 67$