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) (b) find ( m angle f ).

Explanation:

Step1: Determine the type of triangle in part (a)

Since all angles in triangle \(ABC\) are \(60^{\circ}\), it is an equilateral triangle. In an equilateral triangle, all sides are equal. Given \(BC = 6\), so \(AB=6\).

Step2: Determine the type of triangle in part (b)

In triangle \(DEF\), two sides are marked as equal (isosceles triangle property: angles opposite equal sides are equal). Let \(\angle D=\angle F\). Using the angle - sum property of a triangle (\(\angle D+\angle E+\angle F = 180^{\circ}\)). Given \(\angle E = 40^{\circ}\), then \(2\angle F=180^{\circ}- 40^{\circ}\). So \(\angle F=\frac{180 - 40}{2}=70^{\circ}\)

Answer:

(a) \(AB = 6\)
(b) \(m\angle F=70^{\circ}\)