Question

these figures are congruent. what is ( mangle e )?

Explanation:

Step1: Find quadrilateral angle sum

The sum of interior angles of a quadrilateral is $(4-2)\times180^\circ = 360^\circ$.

Step2: Identify congruent angle pairs

Since the figures are congruent, $\angle D \cong \angle P = 62^\circ$, $\angle C \cong \angle Q = 92^\circ$, $\angle F \cong \angle N = 56^\circ$.

Step3: Calculate $m\angle E$

Subtract the sum of the other three angles from $360^\circ$.
$m\angle E = 360^\circ - (62^\circ + 92^\circ + 56^\circ)$
$m\angle E = 360^\circ - 210^\circ$

Answer:

$150^\circ$