Question

the interior angles formed by the sides of a hexagon have measures that sum to 720°.
what is the measure of angle f?
enter your answer in the box.
$m\angle f=\square ^\circ$
the hexagon has interior angles: $\angle a=(x-60)^\circ$, $\angle b=(x-40)^\circ$, $\angle c=130^\circ$, $\angle d=120^\circ$, $\angle e=110^\circ$, $\angle f=(x-20)^\circ$

Explanation:

Step1: Sum all interior angles

$(x-60)^\circ + (x-40)^\circ + 130^\circ + 120^\circ + 110^\circ + (x-20)^\circ = 720^\circ$

Step2: Simplify the left side

Combine like terms:
$3x - 60 - 40 - 20 + 130 + 120 + 110 = 720$
$3x + 240 = 720$

Step3: Solve for $x$

Subtract 240 from both sides:
$3x = 720 - 240$
$3x = 480$
Divide by 3:
$x = \frac{480}{3} = 160$

Step4: Calculate $\angle F$

Substitute $x=160$ into $(x-20)^\circ$:
$\angle F = 160 - 20 = 140$

Answer:

$140$