Question

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

Explanation:

Step1: Use rhombus consecutive angle property

Consecutive angles in a rhombus are supplementary, so $m\angle R + m\angle Q = 180^\circ$, and opposite angles are equal: $m\angle R = m\angle T$, so $2u-50^\circ + u = 180^\circ$.

Step2: Solve for $u$

Combine like terms: $3u - 50^\circ = 180^\circ$
Add $50^\circ$ to both sides: $3u = 230^\circ$
Calculate $u$: $u = \frac{230^\circ}{3}$

Step3: Find $m\angle R$

Substitute $u$ into $m\angle R$: $m\angle R = 2\times\frac{230^\circ}{3} - 50^\circ = \frac{460^\circ}{3} - \frac{150^\circ}{3} = \frac{310^\circ}{3}$

Step4: Calculate $m\angle Q$

Use supplementary angle rule: $m\angle Q = 180^\circ - \frac{310^\circ}{3} = \frac{540^\circ}{3} - \frac{310^\circ}{3}$

Answer:

$\frac{230}{3}$ or approximately $76.67^\circ$