consider $ \triangle a b c $ and $ \triangle d e f $ shown below.

answer the following questions.

(a) in $ \triangle a b c, m \angle a=30^{circ} $ and $ m \angle b=64^{circ} $.
in $ \triangle d e f, m \angle d=29^{circ} $ and $ m \angle e=47^{circ} $.
use this information to find the following angle measures.
$ m \angle c= $ $ { }^{circ} $
$ m \angle f= $ $ { }^{circ} $

(b) use the ruler to find all side lengths for each triangle.
assume all lengths are whole numbers.
$ a b= $ $ b c= $ $ c a= $
$ d e= $ $ e f= $ $ f d= $

(c) find the following ratios.
write your answers in simplest form.
$ \frac{a b}{d e}= $ $ \frac{b c}{e f}= $ $ \frac{c a}{f d}= $

(d) three pairs of statements are shown below.
for each pair, select the true statement.
$ \bigcirc $ the angles in $ \triangle a b c $ have the same measures as the angles in $ \triangle d e f $.
$ \bigcirc $ the angles in $ \triangle a b c $ do not have the same measures as the angles in $ \triangle d e f $.
$ \bigcirc $ the ratios of corresponding side lengths are all equal to each other.
$ \bigcirc $ the ratios of corresponding side lengths are not all equal to each other.
$ \bigcirc $ the triangles are similar.
$ \bigcirc $ the triangles are not similar.

Question

consider $ \triangle a b c $ and $ \triangle d e f $ shown below.

answer the following questions.

(a) in $ \triangle a b c, m \angle a=30^{circ} $ and $ m \angle b=64^{circ} $.
in $ \triangle d e f, m \angle d=29^{circ} $ and $ m \angle e=47^{circ} $.
use this information to find the following angle measures.
$ m \angle c= $ $ { }^{circ} $
$ m \angle f= $ $ { }^{circ} $

(b) use the ruler to find all side lengths for each triangle.
assume all lengths are whole numbers.
$ a b= $ $ b c= $ $ c a= $
$ d e= $ $ e f= $ $ f d= $

(c) find the following ratios.
write your answers in simplest form.
$ \frac{a b}{d e}= $ $ \frac{b c}{e f}= $ $ \frac{c a}{f d}= $

(d) three pairs of statements are shown below.
for each pair, select the true statement.
$ \bigcirc $ the angles in $ \triangle a b c $ have the same measures as the angles in $ \triangle d e f $.
$ \bigcirc $ the angles in $ \triangle a b c $ do not have the same measures as the angles in $ \triangle d e f $.
$ \bigcirc $ the ratios of corresponding side lengths are all equal to each other.
$ \bigcirc $ the ratios of corresponding side lengths are not all equal to each other.
$ \bigcirc $ the triangles are similar.
$ \bigcirc $ the triangles are not similar.

Accepted Answer

# Explanation:
## Step1: Calcular $m\angle C$
La suma de los ángulos internos de un triángulo es $180^{\circ}$. En $\triangle ABC$, $m\angle A = 30^{\circ}$ y $m\angle B=64^{\circ}$. Entonces $m\angle C=180^{\circ}-(m\angle A + m\angle B)$.
$m\angle C = 180^{\circ}-(30^{\circ}+64^{\circ})=180^{\circ}-94^{\circ}=86^{\circ}$

## Step2: Calcular $m\angle F$
En $\triangle DEF$, $m\angle D = 29^{\circ}$ y $m\angle E = 47^{\circ}$. Usando la suma de ángulos internos ($180^{\circ}$), $m\angle F=180^{\circ}-(m\angle D + m\angle E)$.
$m\angle F=180^{\circ}-(29^{\circ}+47^{\circ})=180^{\circ}-76^{\circ}=104^{\circ}$

# Answer:
$m\angle C = 86^{\circ}$, $m\angle F = 104^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Calcular \(m\angle C\)

Step2: Calcular \(m\angle F\)

Answer: