Question

1. in parallelogram cdef, side de is extended through e to point g. if m∠feg = 156°, then find m∠c.

Explanation:

Step1: Find adjacent - angle to ∠FEG

Since ∠FEG and ∠DEF form a linear - pair (sum of angles on a straight line is 180°), we can find ∠DEF.
$m\angle DEF=180^{\circ}-m\angle FEG$.
Substitute $m\angle FEG = 156^{\circ}$ into the formula: $m\angle DEF=180 - 156=24^{\circ}$.

Step2: Use property of parallelogram

In parallelogram CDEF, opposite angles are equal. ∠C and ∠DEF are opposite angles.
So, $m\angle C=m\angle DEF$.

Answer:

$24^{\circ}$