Question

bcde ~ vstu. what are m∠e and m∠v?
d
47°
c
e
60°
b
s
125°
v
128°
u
t
m∠e = □°
m∠v = □°
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Explanation:

Step1: Recall quadrilateral angle sum

The sum of interior angles of a quadrilateral is $360^\circ$.

Step2: Identify congruent angles (similarity)

For similar figures $BCDE \sim VSTU$, corresponding angles are equal:
$\angle B \cong \angle V$, $\angle C \cong \angle S$, $\angle D \cong \angle T$, $\angle E \cong \angle U$

Step3: Find $m\angle E$

$\angle E$ corresponds to $\angle U$, so $m\angle E = m\angle U = 128^\circ$

Step4: Calculate $m\angle V$

First, find $m\angle B$ using angle sum of $BCDE$:
$$m\angle B = 360^\circ - m\angle C - m\angle D - m\angle E$$
Substitute known values: $m\angle C = m\angle S = 125^\circ$, $m\angle D = 47^\circ$, $m\angle E = 128^\circ$
$$m\angle B = 360^\circ - 125^\circ - 47^\circ - 128^\circ = 60^\circ$$
Since $\angle V$ corresponds to $\angle B$, $m\angle V = 60^\circ$

Answer:

$m\angle E = 128^\circ$, $m\angle V = 125^\circ$