Angle Sum Property of a Polygon
Trending Questions
Find the angle measure x in the following figures:
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Find the measure of each angle of a regular octagon.
The sum of all interior angles of a regular polygon is 1080∘. What is the measure of each of its interior angles ?
(a) 135∘ (b) 120∘ (c) 156∘ (d) 144∘
Prove that if both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. [3 MARKS]
In a regular polygon, each interior angle is thrice the exterior angle. The number of sides of the polygon is
(a) 6 (b) 8 (c) 10 (d) 12
Find the measure of each interior angle of a regular polygon having (i) 10 sides (ii) 15 sides
What is the maximum number of obtuse angles that a quadrilateral can have?
a) 1
b) 2
c) 3
d) 4
Two alternate sides of a regular polygon, when produced, meet at the right angle, Calculate the number of sides in the polygon.
A quadrilateral has all its four angles of the same measure. What is the measure of each?
The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.
Each interior angle of a regular decagon (a) 60∘ (b) 120∘ (c) 144 ∘ (d) 180 ∘
Find the complement angle of .
ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC=90o.
What is the minimum interior angle possible for a regular polygon? why?
A quadrilateral has three acute angles each measures 80∘. What is the measure of fourth angle?
Is it possible to have a regular polygon each of whose interior angles is 100∘?
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.
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.
Find the number of sides in a polygon if the sum of its interior angles is :
(i) 900o
(ii) 1620o
(iii) 16 right - angles
(iv) right - angles.
In a hexagon ABCDEF, side AB is parallel to side FE and ∠B:∠C:∠D:∠E=6:4:2:3. Find ∠B and ∠D.
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 60o.
In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively.
Show that :
∠AOB=12(∠C+∠D)
In quadrilateral ABCD, side AB is parallel to side DC. If ∠A:∠D=1:2 and ∠C:∠B=4:5
(i) Calculate each angle of the quadrilateral.
(ii) Assign a special name to quadrilateral ABCD.
The angles of a quadrilateral are 110∘, 72∘, 55∘ and x∘. Find the value of x.
State whether the statements are True or False.
A quadrilateral can have all four angles as obtuse.
The angles of a hexagon are x+10o, 2x+20o, 2x−20o, 3x−50o, x+40o, and x+20o. Find x.
Two angles of a quadrilateral are 89o and 113o. If the other two angles are equal; find the equal angles.
The figure, given below, shows a pentagon ABCDE with sides AB and ED parallel to each other, and ∠B:∠C|∠D=5:6:7.
(i) Using formula, find the sum of interior angles of the pentagon.
(ii) Write the value of ∠A+∠E
(iii) Find angles B, C and D.
Calculate the sum of angles of a polygon with :
(i) 10 sides (ii) 12 sides (iii) 20 sides (iv) 25 sides.