Example Question - interior angle formula
Here are examples of questions we've helped users solve.
Calculating Sum of Interior Angles of Convex Polygon
To find the sum of the interior angles of a convex polygon, you can use the following formula: Sum of interior angles = (n - 2) × 180° where n is the number of sides of the polygon. The polygon in the image appears to be a triangle, which has 3 sides. So we substitute n = 3 into the formula: Sum of interior angles = (3 - 2) × 180° Sum of interior angles = 1 × 180° Sum of interior angles = 180° Therefore, the sum of the interior angle measures of this polygon is 180 degrees.
Solving for Number of Sides in a Regular Polygon
To solve this problem, you can use the formula that relates the number of sides of a regular polygon (n) to the measure of its interior angles (A): \[ A = \frac{(n - 2) \times 180°}{n} \] Given that \( A = 140° \), you will need to set up the equation to solve for n: \[ 140° = \frac{(n - 2) \times 180°}{n} \] Multiply both sides by n to clear the fraction: \[ 140n = (n - 2) \times 180 \] Distribute the 180° across the (n - 2): \[ 140n = 180n - 360 \] Then, subtract 180n from both sides to solve for n: \[ -40n = -360 \] Divide both sides by -40: \[ n = \frac{-360}{-40} \] \[ n = 9 \] Therefore, the regular polygon has 9 sides.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com