19.The exterior angle of a regular polygon is 20°.
i) How sides does it have?
ii) What is the measure of each interior angle?
iii) What is the total measure of its angle.
20.What will be the perimeter of a rhombus whose diagonals are 16cm and
12cm respectively
Answers
Answer:
)As it has 20° in its exterior angle and we know the polygon has 360/20 that is 18 sides!!
ii)The measure of each angle is 160 degree
iii)The total measure of its angle is
160×18
that is 2880°
2.Rhombus is a two dimensional shape with four equal sides and four angles which can or cannot be 90∘, but opposite angles are always same, and both diagonals of a rhombus are perpendicular and bisect each other.
Complete step by step answer:
According to given data,(In the attachment)
Shape ABCD is a rhombus and O is the intersecting point of both diagonals which is bisecting both diagonals, and both diagonals are perpendicular to each other according to definition.
⇒AO=162cm=8cm
⇒BO=122cm=6cm
So, ΔAOB is a right triangle, and using Pythagoras Theorem we can find the length of AB which is a side of rhombus.
According to Pythagoras Theorem,
AB²=BO²+AO²
AB=√6²+8²cm
AB=√36+64=√=100=10cm
And we know the perimeter of the rhombus is equal to 4a where ‘a’ is the length of a side.
So, Perimeter of rhombus =4a
=4×10cm=40cm
Hence, the side is 10cm and the perimeter is 40cm.
