Class 8 Equations in Geometry — practice questions with answers

Linear Equations · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. The two angles in the figure form a linear pair. Find x.

A60°
B30°
C45°
D90°

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Answer: C) 45°

Angles on a straight line add to 180°:

x + 3 x = 180

, so

4 x = 180

and

x = 45°

2. Two complementary angles differ by 18°. What is the smaller angle?

A81°
B72°
C54°
D36°

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Answer: D) 36°

Let the smaller be x:

x + (x + 18) = 90

, so

x = 36°

. The larger is 54°.

3. In a triangle, one angle is 20° more than the second, and the third is twice the second. What is the largest angle?

A40°
B90°
C80°
D60°

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Answer: C) 80°

Let the second be x:

x + (x + 20) + 2 x = 180

4 x = 160

x = 40

. Angles 40°, 60°, 80°.

4. An angle is 24° less than its supplement. Find the angle.

A102°
B33°
C57°
D78°

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Answer: D) 78°

x = (180 - x) - 24

, so

2 x = 156

x = 78°

5. A rectangle's length is 8 cm more than its breadth. If the length is reduced by 4 cm and the breadth increased by 2 cm, the area stays the same. What is the breadth?

A12 cm
B8 cm
C4 cm
D2 cm

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Answer: C) 4 cm

Let breadth = b, length = b + 8.

(b + 4) (b + 2) = (b + 8) b

gives

b^{2} + 6 b + 8 = b^{2} + 8 b

, so

2 b = 8

b = 4

cm.

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