Question
Question 13(Multiple Choice Worth 2 points) (Polygon Angle Sums MC) A regular polygon has 12 sides. If one of its angles measures (8h-30)^circ what is the value of h? h=10.75 h=18.75 h=20.25 h=22.5
Solution
4.1
(132 Votos)
Carlos
Profissional · Tutor por 6 anos
Resposta
Explicação
## Step 1The sum of the interior angles of a polygon with
sides is given by the formula \((n-2) \times 180^{\circ}\). For a regular polygon, all angles are equal, so each angle is \(\frac{(n-2) \times 180^{\circ}}{n}\).## Step 2In this case, the polygon has 12 sides, so each angle is \(\frac{(12-2) \times 180^{\circ}}{12} = 150^{\circ}\).## Step 3Given that one of the angles measures \((830)^{\circ}\), we can set this equal to 150 and solve for
:###
## Step 4Adding 30 to both sides gives:###
## Step 5Dividing both sides by 8 gives:###
So, the value of
is 22.5.