# Interior And Exterior Angles

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
| By Kevallwhitley
K
Kevallwhitley
Community Contributor
Quizzes Created: 1 | Total Attempts: 1,137
Questions: 9 | Attempts: 1,137

Settings

Quiz on finding interior and exterior angles of polygons

• 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.

Rate this question:

• 2.

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

• A.

900

• B.

1260

• C.

128.6

• D.

720

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.

Rate this question:

• 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

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.

Rate this question:

• 4.

### The exterior angle of a regular nonagon measures 40 degrees.

• A.

True

• B.

False

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.

Rate this question:

• 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

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.

Rate this question:

• 6.

### Find the sum of anlges in a regular decagon.

• A.

144

• B.

1440

• C.

36

• D.

1800

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.

Rate this question:

• 7.

### Exterior and interior angles are complementary angles.

• A.

True

• B.

False

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.

Rate this question:

• 8.

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

• A.

90

• B.

360

• C.

45

• D.

180

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.

Rate this question:

• 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

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.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

• Current Version
• Mar 18, 2024
Quiz Edited by
ProProfs Editorial Team
• Feb 16, 2011
Quiz Created by
Kevallwhitley

Related Topics