Question

find ( mangle c ) in parallelogram ( abcd ).
( d ) angle: ( 7s - 63^circ ), ( a ) angle: ( 3s - 17^circ )
( mangle c = square^circ )

Explanation:

Step1: Use consecutive angles property

In a parallelogram, consecutive angles are supplementary, so their sum is $180^\circ$.
$$(7s - 63^\circ) + (3s - 17^\circ) = 180^\circ$$

Step2: Simplify and solve for $s$

Combine like terms and isolate $s$.
$$10s - 80^\circ = 180^\circ$$
$$10s = 260^\circ$$
$$s = 26^\circ$$

Step3: Find $\angle A$ first

Substitute $s$ into the expression for $\angle A$.
$$m\angle A = 3(26^\circ) - 17^\circ = 78^\circ - 17^\circ = 61^\circ$$

Step4: Use opposite angles property

In a parallelogram, opposite angles are equal, so $m\angle C = m\angle A$.
$$m\angle C = 61^\circ$$

Answer:

$61$