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 ( mangle f ). ( mangle f = square^circ )

Explanation:

Step1: Identify triangle type (a)

Triangle $ABC$ has all $60^\circ$ angles, so it is equilateral. All sides are equal.

Step2: Solve for $AB$ (a)

Since $BC = 6$ and all sides of an equilateral triangle are equal, $AB = BC = 6$.

Step3: Identify triangle type (b)

Triangle $DEF$ has $DE = FE$ (tick marks), so it is isosceles with $\angle D = \angle F$.

Step4: Calculate $\angle F$ (b)

Sum of angles in a triangle is $180^\circ$. Let $m\angle F = x$. Then $x + x + 40^\circ = 180^\circ$.
Simplify: $2x = 180^\circ - 40^\circ = 140^\circ$, so $x = \frac{140^\circ}{2} = 70^\circ$.

Answer:

$AB = 6$
$m\angle F = 70^\circ$