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7. 

(b) Find x + y + z + w

Here you will find the detailed solution of the above-written question,       Sum of all angles of quadrilateral =  Let the unmarked angle be A.    =   = 

Q7.

 

(a) Find x + y + z

(a) Find Sum of all angles of triangle is  the unmarked angle of triangle be A.                                                                                                                                            =   = 

Q6. Find the angle measure x in the following figures.

    

        (linear pair)                                                                  (linear pair)                                                                                          Sum of all angles of pentagon =   

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

    

This pentagon has all sides and all angles equal. Sum of all angles of pentagon is 

Q6. Find the angle measure x in the following figures.

    

The Solution for the above-written question is mentioned below, Sum of angles of a quadrilateral 

Q6. Find the angle measure x in the following figures.

    

The solution for the above-written question is mentioned below, Sum of angles of a quadrilateral 

Q5. What is a regular polygon? 
State the name of a regular polygon of

    (iii) 6 sides

A regular polygon is a polygon which have equal sides and equal angles. The name of a regular polygon of 6 sides is a hexagon. All angles of the hexagon are  each.

Q5. What is a regular polygon? 
State the name of a regular polygon of

    (ii) 4 sides

A regular polygon is a polygon which has equal sides and equal angles. The name of a regular polygon of 4 sides is square. Square has all angles of and all sides are equal.

Q5. What is a regular polygon?
State the name of a regular polygon of
    (i) 3 sides

A regular polygon is a polygon which has equal sides and equal angles. The name of a regular polygon of 3 sides is an equilateral triangle. All sides of the equilateral triangle are equal and angles are also equal. Each angle = 

Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?

    (d) n

(d) All the angles of a convex polygon added up to  the sum of the angles of a convex polygon having n sides   

4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides? 

    (c) 10

 (c) 10 angle sum of a convex polygon angle sum of a convex polygon with 10 sides  angle sum of a convex polygon with 10 sides  angle sum of a convex polygon with 10 sides 

Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with the number of sides?

    (b) 8

 (b) 8 sum of the angles of a convex polygon sum of the angles of a convex polygon with 8 sides  sum of the angles of a convex polygon with 8 sides  sum of the angles of a convex polygon with 8 sides 

Q4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7

(a) 7 the sum of angles of a convex polygon the sum of angle of a convex polygon with 7 sides  the sum of angles of a convex polygon with 7 sides  the sum of angles of a convex polygon with 7 sides 

Q3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property
hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

The sum of the measures of the angles of a convex quadrilateral is .A convex quadrilateral is made of two triangles and sum of angles of a triangle is .Hence,sum of angles of two triangles is  which is also sum of angles of a quadrilateral. Here,as we can see this quadrilateral has two triangles and sum of angles of these triangles is = sum of all angles of a quadrilateral.

Q2. How many diagonals does each of the following have?

    (c) A triangle

(c) A triangle A triangle does not have any diagonal.

Q2. How many diagonals does each of the following have?

    (b) A regular hexagon

 (b) A regular hexagon : Total number of diagonal a regular hexagon have are 9 .

Q2. How many diagonals does each of the following have?
    (a) A convex quadrilateral

    (a) A convex quadrilateral : There are 2 diagonals in a convex quadrilateral.

Q1. Given here are some figures.


Classify each of them on the basis of the following.

    (e) Concave polygon

(e) Concave polygon : Concave polygon have one or more interior angles greater than .      Concave polygon = 1.

Q1. Given here are some figures.


Classify each of them on the basis of the following.

(d) Convex polygon

  (d) Convex polygon :Convex polygon are polygons having all interior angles less than .        Convex polygon = 2.

Q1. Given here are some figures.


Classify each of them on the basis of the following.

    (c) Polygon

A normally closed curve made up of more than 4 line segments is called a polygon. Some polygons are shown in figures 
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