Question

for each part below, use the figure to fill in the blank. if necessary, you may learn what the markings on a figure indicate. (a) find ab. (b) find m∠f. ab = □ m∠f = □°

Explanation:

Part (a)

Step1: Identify triangle type

Triangle \( ABC \) has all angles \( 60^\circ \), so it's equilateral.

Step2: Equilateral triangle property

In an equilateral triangle, all sides are equal. Given \( BC = 3 \), so \( AB = BC = 3 \).

Step1: Identify triangle type

Triangle \( DEF \) (wait, \( DEF \)? Wait, the triangle is \( DEF \)? Wait, the triangle has \( DE = EF \) (marked with ticks), so it's isosceles with \( DE = EF \). So \( \angle D=\angle F \).

Step2: Sum of angles in triangle

Sum of angles in a triangle is \( 180^\circ \). Given \( \angle E = 110^\circ \), so \( \angle D+\angle F = 180 - 110 = 70^\circ \). Since \( \angle D=\angle F \), each is \( 70/2 = 35^\circ \).

Answer:

\( AB = 3 \)

Part (b)