Question

find ( mangle x ) and ( mangle y ) in rhombus ( wxyz ).
( mangle x = square^circ )
( mangle y = square^circ )

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so their sum is $180^\circ$.
$$(v-7) + (2v-38) = 180$$

Step2: Simplify and solve for $v$

Combine like terms and isolate $v$.
$$3v - 45 = 180$$
$$3v = 225$$
$$v = 75$$

Step3: Calculate $m\angle X$

Substitute $v=75$ into $\angle X$ expression.
$$m\angle X = 75 - 7 = 68$$

Step4: Calculate $m\angle Y$

Substitute $v=75$ into $\angle Y$ expression.
$$m\angle Y = 2(75) - 38 = 150 - 38 = 112$$

Answer:

$m\angle X = 68^\circ$
$m\angle Y = 112^\circ$