Question

find ( mangle c ) in rhombus ( cdef ).
( mangle c = square^circ )
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Explanation:

Step1: Use rhombus consecutive angles property

Consecutive rhombus angles are supplementary: $\angle F + \angle D = 180^\circ$

Step2: Substitute angle expressions

$(5s+11) + (4s+32) = 180$

Step3: Simplify and solve for $s$

$9s + 43 = 180 \implies 9s = 137 \implies s = 15$

Step4: Find $\angle F$ measure

$\angle F = 5(15)+11 = 86^\circ$

Step5: Use rhombus opposite angles property

Opposite rhombus angles are equal: $\angle C = \angle E$, and $\angle C + \angle F = 180^\circ$

Step6: Calculate $\angle C$

$\angle C = 180 - 86 = 101^\circ$

Answer:

$101^\circ$