Question

1. In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2: 3: 4. Find the measure of each angle of the quadrilateral.
2. The interior angle of a regular is 108°. Find the number of sides of the polygon.
3. The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides have the polygon?
4. The measures of two adjacent angles of a parallelogram are in the ratio 4: 5. 5. If an exterior angle of a regular polygon is 45°, then find the number of its sides.
6. If an interior angle of a regular polygon is 162°, then find the number of its sides.
7. Find the measure of an interior angle of a regular polygon having 15 sides.
8. An angle of a parallelogram measures 70°. Find the measure of the remaining three angles. 9. One angle of a quadrilateral is 111° and the remaining three angles are equal. Find three angles.
10. What is the ratio of the interior angles of a pentagon and a decagon?
Who will give wrong answer his/her report will be marked. ​

Answer 1

1.Angles of quadrilateral A, B, C and D are in the ratio 1 : 2 : 3 : 4. Now let, angle A = x. Therefore, angle B = 2x, angle C = 3x and angle D = 4x. Now as we all know that in a quadrilateral the sum of all the angles is equal to 360 degrees.

2.The interior angle of a regular polygon is 108 degrees. So, the exterior angle will be 180-108=72. So, the number of sides of the polygon is 360/72=5.

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