The sum of the interior angle measures of a convex polygon is . How many sides does it have?
Number of sides

Ask by Simmons Cox. in the United States

Mar 25,2025

Question

The sum of the interior angle measures of a convex polygon is $$ 2340^{\circ} $$. How many sides does it have? Number of sides $$ =\square $$

UpStudy AI · Accepted Answer

To find the number of sides of a convex polygon given the sum of its interior angle measures, we can use the formula for the sum of interior angles of a polygon:

$$ \text{Sum of interior angles} = (n - 2) \times 180^{\circ} $$

where $$ n $$ is the number of sides of the polygon.

Given that the sum of the interior angle measures is $$ 2340^{\circ} $$, we can set up the equation:

$$ (n - 2) \times 180^{\circ} = 2340^{\circ} $$

Now, we can solve for $$ n $$ to find the number of sides of the polygon.
Solve the equation by following steps:
- step0: Solve for $$n$$:
  $$\left(n-2\right)\times 180=2340$$
- step1: Multiply the terms:
  $$180\left(n-2\right)=2340$$
- step2: Divide both sides:
  $$\frac{180\left(n-2\right)}{180}=\frac{2340}{180}$$
- step3: Divide the numbers:
  $$n-2=13$$
- step4: Move the constant to the right side:
  $$n=13+2$$
- step5: Add the numbers:
  $$n=15$$
To find the number of sides, use the formula $$ (n - 2) \times 180^{\circ} = 2340^{\circ} $$. Solving this gives $$ n = 15 $$ sides.

The sum of the interior angle measures of a convex polygon is . How many sides does it have?
Number of sides

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The sum of the interior angle measures of a convex polygon is . How many sides does it have? Number of sides