Page 173 - Maths Skills - 7

The Triangle and Its Properties 171

or ∠1 + ∠2 + ∠3 = 540º – 180º

or ∠1 + ∠2 + ∠3 = 360º
Hence, the sum of the exterior angles of a triangle is 360º.

Exercise 10.1

1. Fill in the blanks.

(i) Triangle has ______________ elements.
(ii) A triangle has ______________ vertices, ______________ sides and ______________ angles.

(iii) All the points on the triangle as well as in the interior of the triangle form ______________ region.
(iv) If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the ______________.

(v) All the angles of an equilateral triangle are ______________.
(vi) A triangle has ______________ medians and ______________ altitudes.
(vii) A ______________ connects a vertex of a triangle to the midpoint of the opposite side.

2. Look at each figure below and state whether the triangle is obtuse, acute or right angled.
(i) (ii) (iii) (iv)
48° 60°
30° 75°

90° 42° 120° 30° 45° 60° 60° 60°

3 cm
3. Classify the triangles shown below as scalene, isosceles 4 cm
or equilateral. The length of the sides are given in Figs. (i) 3 cm 4.2 cm 4 cm cm 4.5 cm
to (iii). 2.5
4 cm 3 cm
(i) (ii) (iii)
4. Find the measure of the third angle when the two are given.
(i) 42º, 80º (ii) 45º, 90º (iii) 115º, 35º (vi) 50º, 110º

5. The angles of a triangle are in the ratios given below. Find the measure of each angle.
(i) 1 : 3 : 5 (ii) 4 : 5 : 9 (iii) 2 : 4 : 4 (iv) 1 : 1 : 1

6. The exterior angle and one interior opposite angle of each triangle are given here respectively. Find the
other interior opposite angle and the third angle of each triangle.

(i) 120º, 45º (ii) 95º, 35º (iii) 58º, 20º (iv) 130º, 60º
7. In DABC, if 2∠A = 3∠B = 6∠C, calculate ∠A, ∠B and ∠C.

8. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.
9. One of the acute angles of a right triangle is 48º. Find the other acute angle.

10. One of the exterior angles of a triangle is 120º and the interior opposite angles are in the ratio 4 : 2. Find
the angles of the triangle.

11. If each one of the equal angles of an isosceles triangle is 55º, find the third angle.