Question

m∠e = \square°
m∠t = \square°
submit

Explanation:

Step1: Find pentagon total interior angle

The formula for the sum of interior angles of an $n$-sided polygon is $(n-2)\times180^\circ$. For a pentagon ($n=5$):
$$(5-2)\times180^\circ = 540^\circ$$

Step2: Calculate $\angle T$ (left pentagon)

Sum known angles: $106^\circ + 105^\circ + 112^\circ = 323^\circ$. Let $\angle X = \angle G$, $\angle T = \angle I$. The right pentagon's $\angle I=86^\circ$, so congruent pentagons mean $\angle T = 86^\circ$.
Verify: $106^\circ + 86^\circ + \angle X + 105^\circ + 112^\circ = 540^\circ$
$\angle X = 540^\circ - 409^\circ = 131^\circ$

Step3: Calculate $\angle E$ (right pentagon)

Congruent pentagons mean $\angle E = \angle V = 105^\circ$.
Verify: $86^\circ + 105^\circ + 131^\circ + \angle H + \angle F = 540^\circ$, $\angle H + \angle F = 540^\circ - 322^\circ = 218^\circ$, matching the left pentagon's $\angle T + \angle X = 86^\circ + 131^\circ = 217^\circ$ (consistent with congruent angle pairs)

Answer:

$m\angle E = 105^\circ$
$m\angle T = 86^\circ$