Question

1.
The angles of a quadrilateral are (x-20)° and (2x + 20)° and the remaining angles are 60° and 90°. Find
the measure of two unknown angles.
2. Find the measure of each exterior angle of a regular polygon of 6 sides and 18 sides.
​

Answer 1

1]

Given :-

The angles of a quadrilateral are (x-20)° and (2x + 20)° and the remaining angles are 60° and 90°

To Find :-

Unknown angle

Solution :-

Sum of all angle is 360

x - 20 + 2x + 20 + 60 + 90 = 360

3x + 60 + 90 = 360

3x + 150 = 360

3x = 360 - 150

3x = 210

x = 210/3

x = 70

Angles are

x - 20 = 70 - 20 = 50°

2x + 20 = 2(70) + 20 = 140 + 20 = 160

2]

Given :-

Regular polygon of 6 sides and 18 sides.

​To Find :-

Measue of exterior angle

Solution :-

For 6 sides

Exterior angle = 360/n

Exterior angle = 360/6

Exterior angle = 60°

For 18 sides

Exterior angle = 360/n

Exterior angle = 360/18

Exterior angle = 20°

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Answer 2

1]

Given :-

The angles of a quadrilateral are (x-20)° and (2x + 20)° and the remaining angles are 60° and 90°

To Find :-

Unknown angle

Solution :-

Sum of all angle is 360

x - 20 + 2x + 20 + 60 + 90 = 360

3x + 60 + 90 = 360

3x + 150 = 360

3x = 360 - 150

3x = 210

x = 210/3

x = 70

Angles are

x - 20 = 70 - 20 = 50°

2x + 20 = 2(70) + 20 = 140 + 20 = 160

2]

Given :-

Regular polygon of 6 sides and 18 sides.

To Find :-

Measue of exterior angle

Solution :-

For 6 sides

Exterior angle = 360/n

Exterior angle = 360/6

Exterior angle = 60°

For 18 sides

Exterior angle = 360/n

Exterior angle = 360/18

Exterior angle = 20°