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CBSE · Class 7 · Mathematics

A Tale of Three Intersecting Lines

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
Can 4 cm, 8 cm and 16 cm be the sides of a triangle?
  1. Only if it is right-angled
  2. Yes
  3. Only if two sides are equal
  4. No
2.
Two angles of a triangle are 120° and 33°. The third angle is:
  1. 27°
  2. 207°
  3. 87°
  4. 37°
3.
The three angles of a triangle add up to:
  1. 270°
  2. 90°
  3. 180°
  4. 360°
4.
The two interior angles opposite an exterior angle of a triangle are 34° and 51°. The exterior angle is:
  1. 17°
  2. 146°
  3. 95°
  4. 85°
5.
A triangle has angles 81°, 54°, 45°. It is:
  1. acute-angled
  2. equilateral
  3. right-angled
  4. obtuse-angled
6.
The angle between the equal sides of an isosceles triangle is 150°. Each base angle is:
  1. 150°
  2. 30°
  3. 75°
  4. 15°
7.
Can 3 cm, 4 cm and 8 cm be the sides of a triangle?
  1. Only if drawn carefully
  2. Yes
  3. Only if one angle is 90°
  4. No
8.
Two sides of a triangle are 8 cm and 16 cm. Which of these could be the third side?
  1. 30 cm
  2. 8 cm
  3. 11 cm
  4. 24 cm
Section B — Short answer8 × 2 = 16 marks
9.
The angles of a triangle are x, x + 29° and x + 34°. Find x and the three angles.
10.
An exterior angle of a triangle is 100° and one of the opposite interior angles is 74°. Find the other opposite interior angle and the angle next to the exterior angle.
11.
The angles of a triangle are in the ratio 4 : 7 : 1. Find them.
12.
Two sides of a triangle are 16 cm and 19 cm. Between which two lengths must the third side lie?
13.
Each base angle of an isosceles triangle is 82°. Find the third angle, and say whether the triangle is acute, right or obtuse.
14.
One acute angle of a right-angled triangle is 62°. Find the other acute angle.
15.
Which of these can be the sides of a triangle? (i) 10, 6, 20 (ii) 9, 10, 19 (iii) 11, 5, 16 (all in cm)
16.
In triangle PQR, ∠P = 70° and ∠Q = 58°. The side QR is extended beyond R. Find the exterior angle at R.
Section C — Word problems4 × 4 = 16 marks
17.
Isha has three fence pieces of 7 m, 17 m and 18 m. Can they make a triangular pen? If yes, what is its perimeter?
18.
A roof frame is an isosceles triangle with the two equal sloping beams meeting at 88° at the top. What angle does each beam make with the floor beam?
19.
A ramp rises from the ground, making 18° with it, and meets a vertical wall at a right angle to the ground. What angle does the ramp make with the wall?
20.
Village A is 13 km from village B, and B is 14 km from village C. The direct road from A to C is 16 km. How much shorter is the direct road than going through B?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 7 · Mathematics

Answer key

A Tale of Three Intersecting Lines · AW-7M-TRI-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) No4 + 8 is not more than 16
2(a) 27°180° − 153°
3(c) 180°—
4(d) 85°34° + 51°
5(a) acute-angledthe largest angle is 81°
6(d) 15°(180° − 150°) ÷ 2
7(d) No3 + 4 is less than 8
8(c) 11 cmthe third side is between 8 cm and 24 cm
9x = 39°; 39°, 68°, 73°3x + 63° = 180°; 3x = 117°
1026°; 80°100° − 74°; 180° − 100°
1160°, 105°, 15°180° ÷ 12 = 15°
12more than 3 cm and less than 35 cm19 − 16 and 16 + 19
1316°; acute180° − 2 × 82°
1428°90° − 62°
15(i) no, (ii) no, (iii) nocheck that the two shorter sides add up to more than the longest
16128°it equals the sum of the two opposite interior angles
17Yes; 42 mevery two pieces together are longer than the third
1846°(180° − 88°) ÷ 2
1972°the angles of the triangle add to 180°: 180° − 90° − 18°
2011 km shorter13 + 14 − 16; the direct side is always shorter