Question

find $m\angle cdf$ and $m\angle def$.
$(5x + 2)^\circ$
$(2x + 18)^\circ$
$m\angle cdf =$ number
$m\angle def =$ color

Explanation:

Step1: Set angles equal (alternate interior)

$5x + 2 = 2x + 18$

Step2: Solve for x

$5x - 2x = 18 - 2$
$3x = 16$
$x = \frac{16}{3} \approx 5.33$

Step3: Calculate $m\angle CDF$

$m\angle CDF = 5x + 2 = 5\times\frac{16}{3} + 2 = \frac{80}{3} + \frac{6}{3} = \frac{86}{3} \approx 28.67^\circ$

Step4: Find supplementary angle for $\angle DEF$

First find $\angle CDE$: $\angle CDE = 180^\circ - (5x+2)^\circ = 180 - \frac{86}{3} = \frac{540 - 86}{3} = \frac{454}{3}^\circ$
In parallelogram $CDEF$, $\angle DEF = \angle CDF = \frac{86}{3}^\circ$ (opposite angles of parallelogram are equal)

Answer:

$m\angle CDF = \frac{86}{3}^\circ \approx 28.7^\circ$
$m\angle DEF = \frac{86}{3}^\circ \approx 28.7^\circ$