1. What is the sum of the interior angles of a polygon having 9 sides?
2. What is the measure of each exterior angle of a regular polygon having 10 sides?
3. The angles of a quadrilateral are respectively 100°, 98°, 92°. Find the fourth angle.
4. In a quadrilateral, the angles A, B, C and D are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle of the quadrilateral.
5. How many sides does a regular polygon have if the measure of an exterior angle is 24°?
6. What is a parallelogram whose all sides are equal is called?
7. What is the sum of the interior angles of a polygon having 9 sides?
8. What is the measure of each exterior angle of a regular polygon having 10 sides?
9. The angles of a quadrilateral are respectively 100°, 98°, 92°. Find the fourth angle.
10. In a quadrilateral, the angles A, B, C and D are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle of the quadrilateral.
Answers
Answer:
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Step-by-step explanation:
1. Sum of interior angles in a polygon = (n-2)180
n = 9
(9-2)180
= 7×180
= 1260
2. Sum of exterior angles in a polygon = 360
A regular polygon has equal sides and angles.
Let the value of a angle be x
No. of sides = 10
10x = 360
x = 360 ÷ 10
= 36
3. Sum of angles in a quadrilateral = 360
Fourth angle = 360 - (100+98+92)
= 360 - 290
= 70
4. Sum of angles in a quadrilateral = 360
angle A = x
angle B = 2x
angle C = 3x
angle D = 4x
x+2x+3x+4x = 360
10x = 360
x = 360 ÷ 10
= 36
5. Sum of exterior angles in a polygon = 360
One exterior angle = 24
It is a regular polygon
Therefore, No. of sides = 360 ÷ 24
= 15
6. Rhombus
7. n = 9
(9-2)180
= 7×180
= 1260
8. Sum of exterior angles in a polygon = 360
A regular polygon has equal sides and angles.
Let the value of a angle be x
No. of sides = 10
10x = 360
x = 360 ÷ 10
= 36
9. Sum of angles in a quadrilateral = 360
Fourth angle = 360 - (100+98+92)
= 360 - 290
= 70
10. Sum of angles in a quadrilateral = 360
angle A = x
angle B = 2x
angle C = 3x
angle D = 4x
x+2x+3x+4x = 360
10x = 360
x = 360 ÷ 10
= 36