## Chapter 6 Triangle and its Properties Exercise 6.3

**Question 1: Find the value of the unknown x in the following diagrams:(i)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 50° + 60° + x

= 180° – (50° + 60°)

= 180° - 110° = 70°

= x = 70°

Therefore, by angle sum property x = 70°.

**(ii)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 90° + 30° + x

= 180° - (90° + 30°)

= 180° - 120° = 60°

= x = 60°

Therefore, by angle sum property x = 60°.

**(iii)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 110° + 30° + x

= 180° – (110° + 30°)

= 180° - 140° = 40°

= x = 40°

Therefore, by angle sum property x = 40°.

**(iv)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 50° + x + x

= 180° – 50°

= 130° = x + x

= 130° = 2x

= 130/2 = 65°

= x = 65°

Therefore, by angle sum property x = 65° each.

**(v)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = x + x + x

= 180° = 3x

= 180/3 = 60°

= x = 60°

Therefore, by angle sum property x = 60° each.

**(vi)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 90° + 2x + x

= 180° – 90°

= 90° = x + 2x

= 90° = 3x

= 90/3 = 30°

= 2x = 30 x 2 = 60°

Therefore, by angle sum property x = 30° while 2x = 60°.

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

(i)

(i)

**Answer:**

(by sum of 2 interior opposite angle is equal to exterior angle)

= 50° + x = 120°

= 120° - 50° = 70°

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 50° + 70° + y

= 180° - (50° + 70°)

= 180° - 120°

= 60° = y

Therefore, x = 70° while y = 60°.

**(ii)**

**Answer:**

(by vertically opposite angles are equal)

= 80° = y = 80°

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 50° + 80° + x

= 180° - (50° + 80°)

= 180° - 130°

= 50° = x

Therefore, x = 50° while y = 80°.

**(iii)**

**Answer:**

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 50° + 60° + y

= 180° - (50° + 60°)

= 180° - 110°

= 70° = y

(by sum of 2 interior opposite angles is equal to exterior angle)

= 50° + 60° = x

= 110° = x

Therefore, x = 110° while y = 70°.

**(iv)**

**Answer:**

(by vertically opposite angle are equal)

= 60° = x = 60°

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 30° + 60° + y

= 180° - (30° + 60°)

= 180° - 90°

= 90° = y

Therefore, x = 60° while y = 90°.

**(v)**

**Answer:**

(by vertically opposite angle are equal)

= 90° = y = 90°

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = 90° + x + x

= 180° - 90°

= 90°

= 90° = x + x

= 90° = 2x

= 90/2 = 45°

Therefore, x = 45° each while y = 90°.

**(vi)**

**Answer:**

(by vertically opposite angle are equal)

= y = x

(by angle sum property)

Sum of 3 angles of triangle = 180°

= 180° = x + x + x

= 180° = 3x

= 180/3 = 60°

Therefore, x = 60° each while y = 60°.

## No comments:

## Post a Comment