Question

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

Explanation:

Step1: Sum of quadrilateral angles

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

Step2: Match congruent angles (similarity)

Since $BCDE \sim VSTU$, corresponding angles are congruent:
$m\angle B = m\angle U = 60^\circ$, $m\angle D = m\angle T = 47^\circ$, $m\angle C = m\angle S = 125^\circ$, $m\angle E = m\angle U = 128^\circ$.

Step3: Calculate $m\angle V$

Use angle sum for $VSTU$:
$m\angle V = 360^\circ - m\angle S - m\angle T - m\angle U$
$m\angle V = 360^\circ - 125^\circ - 47^\circ - 60^\circ = 127^\circ$

Answer:

$m\angle E = 128^\circ$, $m\angle V = 127^\circ$