Page 180 - ICSE Math 7

EXERCISE 16.1

1. Which of the following sets can be three angles of a triangle?

(a) 45°, 40°, 80° (b) 60°, 50°, 70° (c) 55°, 75°, 50°
2. Find the unknown angle and classify the triangle on the basis of angles.
(a) ∠R = 95°, ∠Q = 45° (b) ∠A = 65°, ∠B = 35° (c) ∠A = ∠B = 80°

(d) ∠P = 140°, ∠Q = ∠R (e) ∠B – ∠C = 40°, ∠B = 80°
3. The angles of a triangle are in the ratio 3 : 1 : 2. Find the angles and classify the triangle.
4. Find the unknown angles in the following figures.
N

A P P 3x R

(a) 5x (b) x (c) x – 10° (d)
B 3x 2x C Q x x R 2x
L 30° x + 10° M Q
5. One angle of a triangle is 70° and the other two angles are in the ratio 5 : 6. Find these angles.
6. Use the properties of triangles to find the unknown angles.

x
65°
y 116°
(a) x (b) 50° (c) x (d)
110°
x
40° 50° y

7. Check whether DABC is equilateral or isosceles.
(a) ∠A = x + 30°, ∠B = 2x + 5°, ∠C = 3x – 5°
(b) ∠A = y + 20°, ∠B = 2y – 20°, ∠C = 3y – 60°

(c) ∠A = 2x + 2°, ∠B = 3x – 12°, ∠C = 8x + 8°
8. The ratio between the base angle and the vertical angle of an isosceles triangle is 2 : 5. Find each
angle of the triangle.

Pythagoras Property (or Pythagoras Theorem) A

In a right-angled triangle, the side opposite the right angle is Hypotenuse
known as hypotenuse and the other two sides containing the Perpendicular
right angle are called its legs or simply referred to as base and
perpendicular. B Base C

Pythagoras property
In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares
of the other two sides. Therefore, in a right-angled ∆ ABC having right angle at B, we have
2
2
2
AC = AB + BC .
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