# Tutor profile: Bonnie G.

## Questions

### Subject: Geometry

What is the measure of an interior angle and exterior angle of a regular decagon?

Step 1 is to find the sum of the angles of a decagon. You can draw a decagon (10 sides) and connect lines from one vertex to another without overlapping lines. When you do this, you will end up with 8 triangles inside the decagon. Since triangles have 180 degrees each, the decagon will have 180 degrees * 8 or a sum of 1440 degrees interior angles. Another way to do this is to take the number of sides of the decagon (10 sides). Subtract 2 from 10, and then multiply by 180. This method will also work too. (You will always subtract 2 and then multiply by 180). So you know the sum of the interior angles is 1440. Since there are 10 angles, you will divide 1440 by 10 to get 144. (Any regular polygon has all angles equal) The measure of an interior angle is 144 degrees. Now to find the measure of an exterior angle, you take 144 and subtract it from 180. You will always subtract from 180 because when you combine an interior angle and an exterior angle, you form a straight line which measures 180 degrees. The measure of an exterior angle is 180 - 144 or 36 degrees. Check exterior angle answer: If you add up all the exterior angles, they will always equal 360 degrees because they form a circle. 36 degrees * 10 angles = 360 degrees.

### Subject: Pre-Algebra

The sum of 3 consecutive numbers is 42. What is the middle number?

Consecutive numbers are numbers that fall one after another...1,2,3,4, etc. Let's call the first number "x". That makes the second number "x + 1". That makes the third number "x + 2". Use this information to write an equation and solve for x. Then you can solve for all 3 numbers. x + x + 1 + x + 2 = 42 Combine like terms 3x + 3 = 42 subtract 3 from both sides 3x = 39 divide both sides by 3 x = 13 This makes 13 the first number, 14 the second number, and 15 the third number. Check your work: 13 + 14 + 15 = 42 ...... yes The question asks for the middle number which is 14.

### Subject: Basic Math

Spirit Middle School will be taking their students on a field trip to the zoo. The secretary has to reserve enough buses for the trip to accommodate 142 students and 13 adults. How many buses should the secretary reserve if each bus can hold 38 passengers?

The secretary will need to reserve 5 buses. 142+13 = 155 passengers 155 passengers total divided by 38 passengers per bus = 4.07 buses You must round UP to the next whole number instead of rounding to the nearest whole number. The reason for rounding up is that 4 buses will only hold 152 passengers, but you need buses for 155 passengers.

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