Question

find ( mangle r ) in rhombus ( qrst ).
( mangle r = square^circ )

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(3v+30^\circ)+(7v-26^\circ)=180^\circ$$

Step2: Simplify and solve for $v$

Combine like terms and isolate $v$:
$$10v + 4^\circ=180^\circ$$
$$10v=176^\circ$$
$$v=17.6^\circ$$

Step3: Substitute $v$ into $\angle R$ expression

Calculate $m\angle R$ using $7v-26^\circ$:
$$m\angle R=7(17.6^\circ)-26^\circ$$
$$m\angle R=123.2^\circ-26^\circ$$

Answer:

$97.2^\circ$