Question

find the measure of the angle indicated. 6) find m∠f.

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $19x - 2=(7x + 14)+80$.

Step2: Simplify the equation

$19x-2=7x + 94$. Subtract $7x$ from both sides: $19x-7x-2=7x-7x + 94$, which gives $12x-2 = 94$. Then add 2 to both sides: $12x-2 + 2=94 + 2$, so $12x=96$.

Step3: Solve for x

Divide both sides by 12: $\frac{12x}{12}=\frac{96}{12}$, so $x = 8$.

Step4: Find the measure of $\angle F$

Substitute $x = 8$ into the expression for $\angle F$: $m\angle F=7x + 14$. Then $m\angle F=7\times8+14=56 + 14=70^{\circ}$.

Answer:

$70^{\circ}$