Class 7 Maths

# Properties of Triangles

## Exercise 6.2

Question 1: Find the value of unknown exterior angle in following diagrams.

(i) x = 50° + 70° = 120°

(ii) x = 65° + 45° = 110°

(iii) x = 30° + 40° = 70°

(iv) x = 60° + 60° = 120°

(v) x = 50° + 50° = 100°

(vi) x = 60° + 30° = 90°

Question 2: Find the value of unknown interior angle in following figures:

Answer: Exterior angle of a triangle is equal to the sum of opposite interior angles.

(i) x = 115° - 50° = 65°

(ii) x = 100° - 70° = 30°

(iii) x = 120° - 60° = 60°

(iv) x = 80° - 30° = 50°

(v) x = 75° - 35° = 40°

### Exercise 6.3

Question 1: Find the value of unknown x in following figures:

(a) Answer: x = 180° - (50° + 60°) = 180° - 110° = 70°

(b) Answer: x = 180° - (30° + 90°)

Since it is a right angle so the third angle is a right angle.

Or, x = 180° - 120° = 60°

(c) Answer: x = 180° - (30° + 110°) = 180° - 140° = 40°

(d) Answer: Here; 50° + 2x = 180°

Or, 2x = 180° - 50° = 130°

Or, x = 130° ÷ 2 = 65°

(e) Answer: This is an equilateral triangle

Hence, 3x = 180°

Or, x = 180° ÷ 3 = 60°

(f) Answer: This is a right angled triangle.

Hence, 2x + x + 90°= 180°

Or, 3x = 180° - 90°

Or, x = 90° ÷ 3 = 30°

Question 2: Find the values of the unknowns x and y in the following diagrams.

(i) Answer: Since an external angle is equal to the sum of opposite exterior angles.

Hence, 120° = 50° + x

Or, x = 120° - 50° = 70°

Now, 120° + y = 180°

Because they make linear pair of angles and angles of a linear pair are always supplementary.

Or, y = 180° - 120° = 60°

(ii) Answer: In this case, y = 80°

Because, vertically opposite angles are always equal.

Now, 50° + y + x = 180° (Angle sum property of triangle)

Or, 50° + 80° + x = 180°

Or, x + 130° = 180°

Or, x = 180° - 130°= 50°

(iii) Answer: Here, x = 50° + 60° = 110°

Because , exterior angle in a triangle is equal to sum of opposite internal angles.

Now, x + y = 180° (Linear pair of angles are supplementary)

Or, 110° + y = 180°

Or, y = 180° - 110° = 70°

(iv) Answer: Here, x = 60° (Vertically opposite angles are equal)

Now, 30° + x + y = 180° (Angle sum of triangle)

Or, 30° + 60° + y = 180°

Or, y + 90° = 180°

Or, y = 180° - 90°

Or, x = 60° and y = 90°

(v) Answer: Here, x = 90° (Vertically opposite angles are equal)

Now, x + x + y = 180°

Or, 2x + 90° = 180°

Or, 2x = 180° - 90° = 90°

Or, x = 90° ÷ 2 = 45°

(vi) Answer: Here, x = y (Vertically opposite angles are equal.

Thus, all angles of the given triangle are equal. It means that the given triangle is equilateral triangle and each angle has same measure.

Hence, x = y = 60°