Angle Sum Property of a Polygon

Q. Question 6
Find the angle measure x in the following figures:

Q. Question 167
Find the measure of each angle of a regular octagon.

Q.

The sum of all interior angles of a regular polygon is ${1080}^{\circ }$. What is the measure of each of its interior angles ?

(a) 135${}^{\circ }$ (b) 120${}^{\circ }$ (c) 156${}^{\circ }$ (d) 144${}^{\circ }$

Q.

Prove that if both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. [3 MARKS]

Q.

Q.

Find the measure of each interior angle of a regular polygon having (i) 10 sides (ii) 15 sides

Q. Question 12
What is the maximum number of obtuse angles that a quadrilateral can have?
a) 1
b) 2
c) 3
d) 4

Q.

Two alternate sides of a regular polygon, when produced, meet at the right angle, Calculate the number of sides in the polygon.

Q.

A quadrilateral has all its four angles of the same measure. What is the measure of each?

Q.

The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

Q.

Each interior angle of a regular decagon (a) 60${}^{\circ }$ (b) 120${}^{\circ }$ (c) 144 ${}^{\circ }$ (d) 180 ${}^{\circ }$

Q.

Find the complement angle of $50°$.

Q.

ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that $\angle AMC={90}^o$.

Q.

What is the minimum interior angle possible for a regular polygon? why?

Q. The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides if the polygon.

Q.

A quadrilateral has three acute angles each measures ${80}^{\circ }$. What is the measure of fourth angle?

Q.

Is it possible to have a regular polygon each of whose interior angles is ${100}^{\circ }$?

Q.

The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.

Q.

The sum of all interior angles of a hexagon is

(a) $6$ right angles.

(b) $8$ right angles.

(c) $9$ right angles.

(d) $12$ right angles.

Q.

Find the number of sides in a polygon if the sum of its interior angles is :

(i) ${900}^o$

(ii) ${1620}^o$

(iii) 16 right - angles

(iv) right - angles.

Q.

In a hexagon ABCDEF, side AB is parallel to side FE and $\angle B:\angle C:\angle D:\angle E=6:4:2:3$. Find $\angle Band\angle D$.

Q.

Calculate the number of sides of a regular polygon, if :

(i) its interior angle is five times its exterior angle.

(ii) the ratio between its exterior angle and interior angle is 2 : 7.

(iii) its exterior angle exceeds its interior angle by ${60}^o$.

Q.

In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively.

Show that :

$\angle AOB=\frac{1}{2}(\angle C+\angle D)$

Q.

In quadrilateral ABCD, side AB is parallel to side DC. If $\angle A:\angle D=1:2and\angle C:\angle B=4:5$

(i) Calculate each angle of the quadrilateral.

(ii) Assign a special name to quadrilateral ABCD.

Q.

The angles of a quadrilateral are ${110}^{\circ },$ ${72}^{\circ },$ ${55}^{\circ }$ and $x^{\circ }$. Find the value of x.

Q. Question 123
State whether the statements are True or False.
A quadrilateral can have all four angles as obtuse.

Q.

The angles of a hexagon are $x+{10}^o,2x+{20}^o,2x-{20}^o,3x-{50}^o,x+{40}^o,andx+{20}^o$. Find x.

Q.

Two angles of a quadrilateral are ${89}^o$ and ${113}^o$. If the other two angles are equal; find the equal angles.

Q.

The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and $\angle B:\angle C|\angle D=5:6:7$.

(i) Using formula, find the sum of interior angles of the pentagon.

(ii) Write the value of $\angle A+\angle E$

(iii) Find angles B, C and D.

Q.

Calculate the sum of angles of a polygon with :

(i) 10 sides (ii) 12 sides (iii) 20 sides (iv) 25 sides.