Question

tuvwx ≅ efghi. what are m∠x and m∠h? m∠x = \\(\square\\)° m∠h = \\(\square\\)° submit

Explanation:

Step1: Find sum of pentagon interior angles

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 $m\angle H$

Congruent polygons have matching angles. $\angle H$ corresponds to $\angle U$, and we solve for $\angle H$ using the total angle sum of the second pentagon:
Let $m\angle H = x$.
$$90^\circ + 120^\circ + 120^\circ + 126^\circ + x = 540^\circ$$
$$456^\circ + x = 540^\circ$$
$$x = 540^\circ - 456^\circ = 84^\circ$$

Step3: Calculate $m\angle X$

$\angle X$ corresponds to $\angle F$, and we solve for $\angle X$ using the total angle sum of the first pentagon:
Let $m\angle X = y$.
$$81^\circ + 123^\circ + y + \text{measure of } \angle U + \text{measure of } \angle V = 540^\circ$$
Since $\angle U = \angle H = 84^\circ$ and $\angle V = \angle E = 120^\circ$:
$$81^\circ + 123^\circ + 84^\circ + 120^\circ + y = 540^\circ$$
$$408^\circ + y = 540^\circ$$
$$y = 540^\circ - 408^\circ = 132^\circ$$

Answer:

$m\angle X = 132^\circ$
$m\angle H = 84^\circ$