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Understanding Quadrilaterals

Question

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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!)

Solution

Solution: The sum of measures of angles of a convex quadrilateral = 360° Yes, this property holds, even if the quadrilateral is not convex.

Some More Questions From Understanding Quadrilaterals Chapter

Given here are some figures.

Classify each of them on the basis of the following.

(a) Simple curve
(b) Simple closed curve
(c) Polygon
(d) Convex polygon
(e) Concave polygon

How many diagonals does each of the following have?

(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle

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!)

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

Figure

Side

3

4

5

6

Angle sum

180°

2 x 180°

= (4 - 2) x 180°

3 x 180°

= (5 - 2) x 180°

4 x 180°

= (6 - 2) x 180°

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

(a) 7 (b) 8 (c) 10 (d) n

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

(i) 3 sides (ii) 4 sides (iii) 6 sides

Find the angle measure x in the following figures.

Find x in the following figures.

Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

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