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 ).
( ab=square )
(b) find ( m angle f ).
( m angle f=square^{circ} )

Explanation:

Step1: Analyze triangle \(ABC\)

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

Step2: Analyze triangle \(DEF\)

In \(\triangle DEF\), \(DE = EF\) (marked with equal - side symbols), so it is an isosceles triangle. The base - angle theorem states that in an isosceles triangle, the base angles are equal. Let \(\angle D=\angle E = 40^{\circ}\). Using the angle - sum property of a triangle (\(\angle D+\angle E+\angle F=180^{\circ}\)).

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Answer:

(a) \(AB = 6\)
(b) \(m\angle F=100^{\circ}\)