Page 164 - Start Up Mathematics_5

Properties of triangles
P
Property 1

The sum of the three angles of a triangle is 180°.

∠P + ∠Q + ∠R = 180°
If the sum of the three angles of a triangle is less than 180°
or more than 180°, the triangle cannot be formed. Q R

Example 1: A set of three angles is given. In each case, Mental Maths
find out whether a triangle can be formed
or not. Guess the measure of each
angle of an equilateral
(a) 100°, 50°, 30° (b) 110°, 95°, 20° triangle.

(c) 90°, 40°, 90° (d) 70°, 65°, 45°
(e) 50°, 45°, 35°

Solution: (a) Angles given are 100° (obtuse), 50° (acute), 30° (acute)

Sum of the three angles = 100° + 50° + 30°
= 180°

So, a triangle can be formed.
(b) Angles given are 110° (obtuse), 95° (obtuse) and 20° (acute).

Sum of the three angles = 110° + 95° + 20°
= 225° > 180°

So, a triangle cannot be formed. Remember
(c) Angles given are 90° (right angle),
40° (acute angle) and 90° (right angle). A triangle cannot have
more than one obtuse or
Sum of the three angles = 90° + 40° + 90° right angle.
= 220° > 180°

So, a triangle cannot be formed.
(d) Angles given are 70° (acute), 65° (acute) and 45° (acute).

Sum of the three angles = 70° + 65° + 45°
= 180°

So, a triangle can be formed.
(e) Angles given are 50° (acute), 45° (acute) Remember
and 35° (acute).

Sum of the three angles = 50° + 45° + 35° One angle of a triangle
must be 60° or more.
= 130° < 180°

So, a triangle cannot be formed.

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