Question

finding angles (level 1)
question
in the diagram below, \\( \overline{ab} \parallel \overline{cd} \\), \\( \overline{ad} \parallel \overline{bc} \\), \\( m\angle eab = 30^\circ \\) and \\( m\angle dea = 64^\circ \\). find \\( m\angle cde \\).
(diagram of a quadrilateral with diagonals intersecting at e, angles labeled 30° at eab and 64° at dea)
answer
attempt 2 out of 2
\\( m\angle cde = \boxed{36} \\)°
submit answer

Explanation:

Step1: Find $\angle ADE$ in $\triangle ADE$

Sum of angles in a triangle is $180^\circ$.
$$\angle ADE = 180^\circ - \angle EAB - \angle DEA = 180^\circ - 30^\circ - 64^\circ = 86^\circ$$

Step2: Use parallel sides to find $\angle ADC$

Since $\overline{AB} \parallel \overline{CD}$ and $\overline{AD}$ is a transversal, alternate interior angles are equal: $\angle ADC = \angle EAB = 30^\circ$

Step3: Calculate $\angle CDE$

Subtract $\angle ADC$ from $\angle ADE$.
$$\angle CDE = \angle ADE - \angle ADC = 86^\circ - 30^\circ = 56^\circ$$

Answer:

$\boldsymbol{56}$