Q. If a pentagon has one angle measuring 120 degrees, what can be inferred about the other angles?
A.
All other angles must also be 120 degrees.
B.
The sum of the other angles must be 360 degrees.
C.
At least one angle must be less than 60 degrees.
D.
The pentagon cannot exist.
Solution
The sum of the interior angles of a pentagon is 540 degrees. If one angle is 120 degrees, the sum of the other four angles must be 540 - 120 = 420 degrees.
Correct Answer:
B
— The sum of the other angles must be 360 degrees.
Q. If a polygon has 10 sides, what is the measure of each interior angle in a regular decagon? (2023)
A.
144 degrees
B.
120 degrees
C.
108 degrees
D.
135 degrees
Solution
The measure of each interior angle in a regular polygon is given by the formula [(n-2) * 180] / n. For a decagon (n=10), it is [(10-2) * 180] / 10 = 144 degrees.
Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular dodecagon?
A.
30 degrees
B.
36 degrees
C.
15 degrees
D.
45 degrees
Solution
The measure of each exterior angle of a regular polygon can be calculated using the formula 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Q. If a polygon has 12 sides, what is the measure of each exterior angle in a regular polygon?
A.
30 degrees
B.
36 degrees
C.
60 degrees
D.
90 degrees
Solution
The measure of each exterior angle of a regular polygon is calculated as 360/n, where n is the number of sides. For a dodecagon (12 sides), it is 360/12 = 30 degrees.
Q. If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
A.
135 degrees
B.
120 degrees
C.
108 degrees
D.
150 degrees
Solution
The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.
Q. If a quadrilateral has one angle measuring 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
40 degrees
C.
60 degrees
D.
80 degrees
Solution
The sum of the angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. If the other three angles are equal, each must be 240/3 = 80 degrees.
Q. In a certain polygon, if one angle measures 120 degrees and the polygon is regular, how many sides does it have?
A.
6
B.
5
C.
8
D.
7
Solution
In a regular polygon, each interior angle can be calculated using the formula (n-2) * 180/n. Setting this equal to 120 degrees and solving for n gives n = 6, indicating a hexagon.
Q. In a regular pentagon, what is the measure of each interior angle?
A.
108 degrees
B.
120 degrees
C.
90 degrees
D.
72 degrees
Solution
The measure of each interior angle in a regular pentagon can be calculated using the formula (n-2) * 180 / n, which results in (5-2) * 180 / 5 = 108 degrees.
Q. In the context of geometry, which of the following statements about polygons is true?
A.
All polygons are convex.
B.
A polygon can have an infinite number of sides.
C.
The sum of the interior angles of a polygon increases with the number of sides.
D.
All polygons are regular.
Solution
The sum of the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides. Therefore, as the number of sides increases, the sum of the interior angles also increases.
Correct Answer:
C
— The sum of the interior angles of a polygon increases with the number of sides.
Polygons are a fundamental concept in geometry that play a crucial role in various school and competitive exams. Understanding polygons not only enhances your mathematical skills but also boosts your confidence in tackling objective questions. Practicing MCQs related to polygons helps in reinforcing concepts and improves your chances of scoring better in exams. With a focus on important questions and practice questions, you can master this topic effectively.
What You Will Practise Here
Definition and properties of polygons
Types of polygons: regular and irregular
Formulas for calculating perimeter and area
Angles in polygons and their sum
Diagonals of polygons and their calculations
Real-life applications of polygons
Visual representations and diagrams of various polygons
Exam Relevance
Polygons are frequently tested in CBSE, State Boards, NEET, and JEE exams. Questions often focus on the properties of different types of polygons, calculations involving their areas and perimeters, and the relationships between angles. Common question patterns include multiple-choice questions that require students to apply formulas and concepts to solve problems efficiently.
Common Mistakes Students Make
Confusing the properties of regular and irregular polygons
Incorrectly calculating the sum of interior angles
Misunderstanding the concept of diagonals in polygons
Overlooking the importance of visual diagrams in problem-solving
FAQs
Question: What is a polygon? Answer: A polygon is a closed figure formed by a finite number of straight line segments connected end to end.
Question: How do you calculate the area of a regular polygon? Answer: The area of a regular polygon can be calculated using the formula: Area = (1/4) * n * s² / tan(π/n), where n is the number of sides and s is the length of a side.
Now is the time to enhance your understanding of polygons! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is key to mastering this topic!
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