Sum of Measures of Exterior Angles of a Polygon

Q. What is the measure of each interior angle of a regular hexagon? How many equilateral triangles can be divided in a regular hexagon?

Q. Question 4
How many sides does a regular polygon have if each of its interior angles is ${165}^{\circ }$?

Q.

The ration of exterior angle to interior angle of a regular polygon is 1:4. Find the numbers of sides of the polygon.

Q.

The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.

Q.

Find the measure of each exterior angle of a regular (i) pentagon (ii) hexagon (iii) heptagon (iv) decagon (v) polygon of 15 sides.

Q.

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :

(i) measure of each interior angle :

(ii) measure of each exterior angle and

(iii) number of sides in the polygon.

Q. The sides of a quadrilateral are produced in order. What is the sum of the four exterior angles?

Q.

In a polygon, each interior angle is thrice the exterior angle. Find the number of sides of the polygon.

Q.

AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = ${20}^o$ ; find :

(i) its each interior angle,

(ii) its each exterior angle

(iii) the number of sides in the polygon.

Q.

The number of sides of a regular polygon whose each interior angle is ${135}^{\circ }$

Q.

Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

Q. Find the number of degrees in each exterior angle of a regular pentagon.

Q.

Find the sum of exterior angles obtained on producing, in order, the sides of a polygon with :

(i) 7 sides (ii) 10 sides (iii) 250 sides

Q.

Proove that interior angle of a regular Pentagon is 3 times the exterior angle of decagon.

Q.

In a regular pentagon ABCDE, draw a diagonal BE and then find the measure of :

(i) $\angle BAE$

(ii) $\angle ABE$

(iii) $\angle BED$

Q.

What is the measure of any exterior angle of a regular nonagon?

Q.

Is it possible to have a regular polygon whose each exterior angle is :

(i) ${80}^o$

(ii) $40\%$ of a right angle.

Q.

Use the following figure to find the value of x.

Q. The interior angle of a polygon is 6 times it's exterior angle. Find the number of sides and the sum of all the interior angle. What is the name of the polygon

Q.

Is it possible to have a regular polygon each of whose exterior angle is ${50}^{\circ }$?

Q.

The angles of a quadrilateral are in the ratio 2:3:4:1.find the measure of each angle of quadrilateral.

Q.

Two angles of a quadrilateral are 72° and 56° respectively and the remaining two angles are in the ratio 3:5 . Find the measure of each angle of the quadrilateral.

Q.

Find the maximum possible exterior angle for a regular polygon

Q.

The exterior angle of a polygon is one-sixth of it's interior angle. What are the angles?

Q.

Three angles of a quadrilateral are in the ratio 2:5:6. If the fourth angle measures 100° , find the other three angles of the quadrilateral.

Q.

If$ a + 10^o, 3a + 10^o, 5a - 10^o $\text{and}$ 3a - 10^o are the angles of a quadrilateral, then what is the value of $a$?

1. 50^o

2. 40^o

3. 30^o

4. 20^o

Q. Question 168
Find the measure of an exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?

Q.

Find the number of sides in a regular polygon, if its each exterior angle is :

(i) $\frac{1}{3}$ of a right angle

(ii) two - fifth of a right - angle.

Q.

The rario between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :

(i) each exterior angle of the polygon ;

(ii) number of sides in the polygon.

Q.

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are $(6x-1{)}^o,(10x+2{)}^o,(8x+2{)}^o(9x-3{)}^o,(5x+4{)}^{o}and(12x+6{)}^o$; find each exterior angle.