Find The Inverse Function Of Gx= 3x-1/2x+3 - Gauthmath

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Question

The interior angle of a given regular polygon is 4 times as big as its exterior angle. How many sides does this polygon have?SHOW LESS0

Solution

user avatar imageAnswer The polygon has 10 sides.ExplanationStep 1: Let \( n \) be the number of sides of the polygon. Step 2: Each exterior angle of an \( n \)-sided polygon is \( \frac{360^\circ}{n} \). Step 3: Each interior angle is 4 times its exterior angle, so each interior angle is \( 4 \times \frac{360^\circ}{n} = \frac{1440^\circ}{n} \). Step 4: Each interior angle plus each exterior angle equals \( 180^\circ \). Step 5: Set up the equation \( \frac{1440^\circ}{n} + \frac{360^\circ}{n} = 180^\circ \). Step 6: Simplify to get \( \frac{1800^\circ}{n} = 180^\circ \). Step 7: Solve for \( n \) to find \( n = \frac{1800^\circ}{180^\circ} \). Click to rate:25.4(63 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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