Interior And Exterior Angles

1.

What is the relationship between any given polygon and the number of triangles that can be drawn inside?

Explanation
Where n is the number of sides (or vertices) of the polygon. This formula calculates the maximum number of triangles that can be formed by connecting any three non-collinear vertices of the polygon.

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2.

If all angles in a heptagon are added together, what would the sum equal?
- A.
  
  900
- B.
  
  1260
- C.
  
  128.6
- D.
  
  720
Correct Answer
A. 900

Explanation
The sum of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides. In the case of a heptagon, which has 7 sides, the sum of the angles would be (7-2) * 180 = 5 * 180 = 900. Therefore, the correct answer is 900.

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3.

If the measures of the angles in a hexagon are as follows, find all the missing angle measures. (Check all answers that are correct)90, 115, x + 75, 2x - 20, x + 10, x
- A.
  
  90
- B.
  
  100
- C.
  
  105
- D.
  
  110
- E.
  
  155
- F.
  
  160
- G.
  
  165
Correct Answer(s)
A. 90
B. 100
F. 160
G. 165

Explanation
The given hexagon has six angles. The first angle is given as 90 degrees. The second angle is given as 115 degrees. The third angle is represented as x + 75. The fourth angle is represented as 2x - 20. The fifth angle is represented as x + 10. The sixth angle is represented as x.

To find the missing angle measures, we can set up equations using the given information.

From the given angles, we have the equation:
90 + 115 + (x + 75) + (2x - 20) + (x + 10) + x = 720

Simplifying the equation, we get:
5x + 270 = 720

Solving for x, we find that x = 90.

Substituting x = 90 into the equations for the missing angle measures, we get:
Third angle = 90 + 75 = 165 degrees
Fourth angle = 2(90) - 20 = 160 degrees
Fifth angle = 90 + 10 = 100 degrees
Sixth angle = 90 degrees

Therefore, the missing angle measures are 100, 160, and 165 degrees.

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4.

The exterior angle of a regular nonagon measures 40 degrees.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
A regular nonagon has 9 sides, so it also has 9 exterior angles. In a regular polygon, all exterior angles are congruent. Therefore, if one exterior angle of a regular nonagon measures 40 degrees, then all the exterior angles of the nonagon must also measure 40 degrees. Therefore, the statement "The exterior angle of a regular nonagon measures 40 degrees" is true.

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5.

In an isoceles, right triangle, what are the measures of the angles?
- A.
  
  90, 30, 60
- B.
  
  100, 40, 40
- C.
  
  60, 60, 60
- D.
  
  90, 45, 45
Correct Answer
D. 90, 45, 45

Explanation
In an isosceles, right triangle, two angles are congruent because the triangle is isosceles. The right angle measures 90 degrees. Since the triangle is isosceles, the remaining two angles are congruent. Therefore, each of those angles measures 45 degrees.

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6.

Find the sum of anlges in a regular decagon.
- A.
  
  144
- B.
  
  1440
- C.
  
  36
- D.
  
  1800
Correct Answer
B. 1440

Explanation
A regular decagon has 10 equal angles. To find the sum of the angles, we can use the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, n = 10, so the sum of the angles is (10-2) * 180 = 8 * 180 = 1440.

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7.

Exterior and interior angles are complementary angles.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
Exterior and interior angles are not complementary angles. Complementary angles are two angles that add up to 90 degrees, while exterior and interior angles are formed by a transversal intersecting two parallel lines. Exterior angles are supplementary to the interior angle adjacent to it, not complementary. Therefore, the correct answer is false.

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8.

In a regular quadrilateral, what is the measure of an interior angle?
- A.
  
  90
- B.
  
  360
- C.
  
  45
- D.
  
  180
Correct Answer
A. 90

Explanation
In a regular quadrilateral, all interior angles are equal. Since a quadrilateral has four angles, the sum of the interior angles is 360 degrees. Therefore, each interior angle in a regular quadrilateral measures 360 degrees divided by 4, which is 90 degrees.

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9.

Listed below are the measures of angles in a polygon. Find the value of x.x, x + 72, x + 80, 100, 120, 45, 80, 100

Correct Answer
161

Explanation
The given question provides a list of angles in a polygon and asks for the value of x. To find x, we can add up all the given angles and subtract them from the sum of angles in a polygon, which is 180 degrees multiplied by (number of sides - 2). In this case, the sum of the given angles is equal to 161 degrees. Therefore, the value of x is 161.

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Interior And Exterior Angles

What is the relationship between any given polygon and the number of triangles that can be drawn inside?

If all angles in a heptagon are added together, what would the sum equal?

If the measures of the angles in a hexagon are as follows, find all the missing angle measures. (Check all answers that are correct)90, 115, x + 75, 2x - 20, x + 10, x

The exterior angle of a regular nonagon measures 40 degrees.

In an isoceles, right triangle, what are the measures of the angles?

Find the sum of anlges in a regular decagon.

Exterior and interior angles are complementary angles.

In a regular quadrilateral, what is the measure of an interior angle?

Listed below are the measures of angles in a polygon. Find the value of x.x, x + 72, x + 80, 100, 120, 45, 80, 100