Practice with Each Interior Angle Topic Index | Geometry Index | Regents Exam Prep Center

 Directions: Choose the correct answer from the choices listed.

 1. Find the measure of each interior angle of a regular decagon. 144° 135° 120° Can't be determined Explanation A decagon has 10 sides, so    n = 10 180(10-2) = 180(8) = 1440 degrees divided by 10 angles = 1440/10 = 144 degrees
 2. How many degrees are there in each interior angle of a hexagon ? 108° 120° 144° Can't be determined Explanation REMEMBER ! We can only use this formula when we have a REGULAR polygon. This question did NOT state that the polygon was regular.
 3. If a regular polygon has 6 sides, how many degrees are there in any one of its angles ? 108° 120° 144° Can't be determined   Explanation n = 6   So the sum is 180(6-2) = 180(4) = 720 Divided by 6 angles 720/6 = 120 degrees
 4. Each interior angle of a regular polygon measures 162°. How many sides does the polygon have ? 20 18 16 Can't be determined Explanation Set the formula equal to 162 180(n-2)/n = 162 Cross multiply 180(n-2) = 162n 180n - 360 = 162n -360 = -18n Divide by  -18 So,  n = 20
 5. How many sides does a regular polygon have if one of its interior angles measures 174° ? 20 40 60 Can't be determined Explanation Set the formula equal to 174 180(n-2)/n = 174 Cross multiply 180(n-2) = 174n 180n - 360 = 174n -360 = -6n Divide by -6 So,  n = 60

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