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Question 13(Multiple Choice Worth 2 Points) (Polygon Angle Sums MC) A Regular Polygon Has 12 Sides. If One of Its Angles Measures

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

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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.