Question

find the value of $x$, $y$, and $z$ in the rhombus below.
$(-8y-5)^\circ$
$(x-7)^\circ$
$(z-8)^\circ$
$75^\circ$
answer attempt 1 out of 2
$x = \square$ $y = \square$ $z = \square$

Explanation:

Step1: Opposite angles of rhombus are equal

$x-7 = 75$

Step2: Solve for $x$

$x = 75 + 7 = 82$

Step3: Adjacent angles of rhombus are supplementary

$-8y-5 + 75 = 180$

Step4: Simplify and solve for $y$

$-8y + 70 = 180$
$-8y = 180 - 70 = 110$
$y = \frac{110}{-8} = -13.75$

Step5: Opposite angles of rhombus are equal

$z-8 = -8y-5$

Step6: Substitute $y=-13.75$, solve for $z$

$z-8 = -8(-13.75)-5 = 110 - 5 = 105$
$z = 105 + 8 = 113$

Answer:

$x = 82$, $y = -13.75$, $z = 113$