Question

quadrilateral qrst is a rhombus and ( mangle qsr = 13c + 5^circ ). what is the value of ( c )?

Explanation:

Step1: Find adjacent angle of $\angle T$

In a rhombus, consecutive angles are supplementary.
$m\angle R = 180^\circ - 118^\circ = 62^\circ$

Step2: Diagonal bisects rhombus angles

Diagonal $QS$ bisects $\angle R$, so $m\angle QSR = \frac{1}{2}m\angle R$
$m\angle QSR = \frac{1}{2} \times 62^\circ = 31^\circ$

Step3: Solve for $c$

Set $13c + 5 = 31$
$13c = 31 - 5 = 26$
$c = \frac{26}{13} = 2$

Answer:

$2$