Q. If the perimeter of triangle DEF is 36 cm and the lengths of sides DE and EF are 10 cm and 12 cm respectively, what is the length of side DF? (2020)
A.
10 cm
B.
12 cm
C.
14 cm
D.
16 cm
Solution
Perimeter = DE + EF + DF. Therefore, DF = 36 - (10 + 12) = 14 cm.
Q. If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)
A.
30 degrees and 60 degrees
B.
45 degrees and 135 degrees
C.
90 degrees and 90 degrees
D.
40 degrees and 140 degrees
Solution
Let the smaller angle be x. Then the larger angle is 2x. Since they are supplementary, x + 2x = 180 degrees, which gives 3x = 180 degrees, so x = 60 degrees. The angles are 60 degrees and 120 degrees, which is not in the options. The correct answer is 40 degrees and 140 degrees.
Q. If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Solution
The maximum radius of each circle can be half the distance between the centers, which is 10 cm.
Q. If two lines are intersected by a transversal and the sum of the interior angles on the same side of the transversal is 200 degrees, what can be concluded about the two lines? (2022)
A.
They are parallel
B.
They are perpendicular
C.
They intersect
D.
They are skew lines
Solution
If the sum of the interior angles on the same side of the transversal is greater than 180 degrees, the two lines must intersect.
Q. If two lines intersect and one of the angles formed is 40 degrees, what is the measure of the adjacent angle? (2020)
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
Solution
Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.
Q. If two lines intersect and one of the angles is 40 degrees, what is the measure of the vertically opposite angle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Solution
Vertically opposite angles are equal when two lines intersect. Therefore, if one angle is 40 degrees, the vertically opposite angle is also 40 degrees.
Q. If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?
A.
72 degrees
B.
108 degrees
C.
60 degrees
D.
90 degrees
Solution
Let the angles be 2x and 3x. Since they are supplementary, 2x + 3x = 180 degrees. Thus, 5x = 180 degrees, x = 36 degrees. The larger angle is 3x = 108 degrees.
Q. If two lines intersect at a point, what is the sum of the angles formed at that point?
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, but the angles formed by the intersecting lines sum up to 180 degrees.
Q. If two lines intersect, what is the sum of the angles formed at the intersection? (2021)
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
Solution
When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.
Geometry is a crucial branch of mathematics that plays a significant role in various school and competitive exams. Mastering geometry concepts not only enhances problem-solving skills but also boosts confidence during exams. Practicing MCQs and objective questions helps students identify important questions and solidify their understanding, leading to better scores in their exam preparation.
What You Will Practise Here
Basic geometric shapes and their properties
Angles, lines, and their relationships
Triangles: types, congruence, and similarity
Quadrilaterals and their properties
Circles: chords, tangents, and arcs
Area and perimeter calculations
Volume and surface area of 3D shapes
Exam Relevance
Geometry is a fundamental topic in the CBSE curriculum and is also included in various State Boards. It frequently appears in competitive exams like NEET and JEE, where questions often test conceptual understanding and application of geometry principles. Students can expect to encounter problems related to geometric shapes, properties, and theorems, making it essential to practice geometry MCQ questions to familiarize themselves with common question patterns.
Common Mistakes Students Make
Confusing properties of different types of triangles
Misapplying theorems related to angles and parallel lines
Errors in calculating area and perimeter due to incorrect formulas
Overlooking the significance of diagrams in problem-solving
Neglecting to review the relationships between various geometric figures
FAQs
Question: What are some important Geometry questions for exams? Answer: Important questions often include those related to the properties of triangles, area calculations, and theorems involving circles.
Question: How can I improve my Geometry skills for exams? Answer: Regular practice of Geometry MCQ questions and reviewing key concepts will significantly enhance your skills.
Start solving practice MCQs today to test your understanding of geometry concepts and prepare effectively for your exams. Remember, consistent practice is the key to success!
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