Question

find the value of x, y and z in the given figures.​

Answer 1

Step-by-step explanation:

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Answer 2

1. By linear pair of angles,

x + 120° = 180°

⇒ x = 180° - 120°

⇒ x = 60°

By exterior angle property,

y + 40° = 120°

⇒y = 120° - 40°

⇒ y = 80°

By linear pair of angles,

y + z = 180°

⇒80° + z = 180°. [ from above]

⇒ z = 180° - 80°

⇒ z = 100°

2. By Alternate interior angles,

z = 45°

By angle sum property of triangle MON

x + 30° + z = 180°

⇒ x + 30° + 45° = 180°

⇒ x + 75° = 180°

⇒ x = 105°

x = y (Vertically opposite angles)

⇒y = 105°

3. By vertically opposite angles,

x = z

y = x

z = y

x + y + z = 180°

Since all angles are equal to each other,

3x = 180°

⇒ x = y = z = 60°

4. By exterior angle property,

60° + z = 110°

⇒ z = 40°

x = 60° (Corresponding angles)

By angle sum property,

x + y + z = 180°

100° + y = 180°

⇒ y = 80°

Additional information:

Some terms used in this problem:

1. Angle Sum property means sum of all angles in a triangle is always 180°.

2. Vertically opposite angles are angles in between the place of intersection of 2 lines.

3. Linear pair of angles means sum of angles on a straight line is 180°.

4. Exterior angle property is the sum of exterior angle with the opposite 2 interior angles in a triangle.