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 ( a b ).
( a b = )
(b) find ( m angle f ).
( m angle f = ) ( circ )

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 \(AB=BC\).

Step2: Find \(m\angle F\) in part (b)

In triangle \(DEF\), \(DE = DF\) (marked as equal). So it is an isosceles triangle. The sum of angles in a triangle is \(180^{\circ}\). Let \(m\angle F=m\angle D\) (base angles of an isosceles triangle). We know \(m\angle E = 40^{\circ}\). Then \(m\angle F=\frac{180 - 40}{2}\).

Answer:

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