Question

(d) Convex polygon (e) Concave polygon
2. How many diagonals does each of the following have?
(a) A convex quadrilateral (b) A regular hexagon (c) Atriangle
3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property​

Answer 1

Answer:

(a) A convex quadrilateral has two diagonals.

(b) A regular hexagon has 9 diagonals.

c) A triangle has no diagonal.

Step-by-step explanation:

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?

Answer:

Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral

( pls note that the diagram is on up of answer)

in two triangles.

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2

= (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)

= 1800 + 1800 [By Angle sum property of triangle]

= 3600

Hence, the sum of measures of the triangles of a convex quadrilateral is 3600.

Yes, if quadrilateral is not convex then, this property will also be applied.