Question

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

Explanation:

Step1: Use rhombus consecutive angle property

Consecutive angles in a rhombus are supplementary, so:
$$(2a+80^\circ)+(6a-20^\circ)=180^\circ$$

Step2: Simplify and solve for $a$

Combine like terms and isolate $a$:
$$8a + 60^\circ = 180^\circ$$
$$8a = 120^\circ$$
$$a = 15^\circ$$

Step3: Substitute $a$ to find $m\angle R$

Plug $a=15^\circ$ into the expression for $\angle R$:
$$m\angle R = 6(15^\circ)-20^\circ$$

Step4: Calculate the final angle value

Compute the numerical result:
$$m\angle R = 90^\circ - 20^\circ = 70^\circ$$

Answer:

$70$