Question

answer the following questions.
(a) in △abc, m∠a = 96° and m∠b = 42°.
in △def, m∠d = 96° and m∠e = 42°.
use this information to find the following angle measures.
m∠c = □°
m∠f = □°
(b) use the ruler to find all side lengths for each triangle.
assume all lengths are whole numbers.
ab = □ bc = □ ca = □
de = □ ef = □ fd = □
(c) find the following ratios.
write your answers in simplest form.
ab/de = □ bc/ef = □ ca/fd = □
(d) three pairs of statements are shown below.
for each pair, select the true statement.
the angles in △abc have the same measures as the angles in △def.

Explanation:

Step1: Find \(m\angle C\) in \(\triangle ABC\)

The sum of angles in a triangle is \(180^{\circ}\). So \(m\angle C=180^{\circ}-m\angle A - m\angle B\).
Substitute \(m\angle A = 96^{\circ}\) and \(m\angle B=42^{\circ}\):
\(m\angle C=180^{\circ}-96^{\circ}-42^{\circ}=42^{\circ}\)

Step2: Find \(m\angle F\) in \(\triangle DEF\)

Using the same angle - sum property (\(180^{\circ}\) for a triangle). \(m\angle F=180^{\circ}-m\angle D - m\angle E\).
Substitute \(m\angle D = 96^{\circ}\) and \(m\angle E = 42^{\circ}\):
\(m\angle F=180^{\circ}-96^{\circ}-42^{\circ}=42^{\circ}\)

Answer:

\(m\angle C = 42^{\circ}\)
\(m\angle F = 42^{\circ}\)