Question

3.
e f g triangle, angle at e is 25°, angle at g is 25°, side gf is 18 in.
ef = ______
m∠f = ______
4.
triangle pqr with all sides marked equal (equilateral triangle).
m∠p = ______
m∠q = ______
m∠r = ______

Explanation:

Step1: Solve for $EF$ (triangle $EFG$)

In $\triangle EFG$, $\angle E = \angle G = 23^\circ$, so it is isosceles with $EF = FG$.
$EF = 18$ m

Step2: Solve for $m\angle F$ (triangle $EFG$)

Sum of angles in a triangle is $180^\circ$.
$m\angle F = 180^\circ - 23^\circ - 23^\circ = 134^\circ$

Step3: Identify triangle $PQR$ type

$\triangle PQR$ has all sides marked equal, so it is equilateral.

Step4: Find angles of equilateral triangle

All angles in an equilateral triangle equal $60^\circ$.
$m\angle P = m\angle Q = m\angle R = 60^\circ$

Answer:

For $\triangle EFG$:
$EF = 18$ m
$m\angle F = 134^\circ$

For $\triangle PQR$:
$m\angle P = 60^\circ$
$m\angle Q = 60^\circ$
$m\angle R = 60^\circ$