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 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 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 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. If angle A and angle B are supplementary, and angle A is 3 times angle B, what is the measure of angle A?
A.
90 degrees
B.
120 degrees
C.
180 degrees
D.
60 degrees
Solution
Let angle B be x. Then angle A = 3x. Since they are supplementary, x + 3x = 180, leading to 4x = 180, so x = 45. Therefore, angle A = 3 * 45 = 135 degrees.
Q. If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?
A.
60 degrees
B.
80 degrees
C.
90 degrees
D.
120 degrees
Solution
Let the angles be 2x, 3x, and 4x. The sum of angles in a triangle is 180 degrees. Therefore, 2x + 3x + 4x = 180. Solving gives x = 20, so the largest angle is 4x = 80 degrees.
Geometry & Mensuration are crucial topics in mathematics that play a significant role in various school and competitive exams. Mastering these concepts not only enhances your problem-solving skills but also boosts your confidence during exams. Practicing MCQs and objective questions helps you familiarize yourself with the exam pattern, making it easier to tackle important questions effectively.
What You Will Practise Here
Understanding basic geometric shapes and their properties
Calculating area and perimeter of various figures
Exploring volume and surface area of 3D shapes
Applying the Pythagorean theorem in problem-solving
Utilizing important formulas for quick calculations
Interpreting diagrams and visual representations
Solving real-life problems using mensuration concepts
Exam Relevance
Geometry & Mensuration are integral parts of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. These topics frequently appear in the form of objective questions and MCQs, often focusing on the application of formulas and theorems. Students can expect questions that require both theoretical understanding and practical application, making it essential to practice regularly to excel in these exams.
Common Mistakes Students Make
Confusing the formulas for area and perimeter
Overlooking units of measurement in calculations
Misinterpreting diagrams, leading to incorrect answers
Neglecting to apply the Pythagorean theorem correctly
Failing to check for the conditions of geometric properties
FAQs
Question: What are the key formulas I should remember for Geometry & Mensuration? Answer: Important formulas include area and perimeter for 2D shapes, volume and surface area for 3D shapes, and the Pythagorean theorem for right-angled triangles.
Question: How can I improve my speed in solving Geometry & Mensuration MCQs? Answer: Regular practice of MCQs and timed quizzes can help improve your speed and accuracy in solving these types of questions.
Start solving practice MCQs today to strengthen your understanding of Geometry & Mensuration. With consistent effort, you can master these topics and achieve your desired scores in exams!
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