Question

Angles of a quadrilateral are in an arithmetic sequence.

a) Find the angle sum.

b) What is the sum of first term and fourth term ?

c) What is the sum of second term and third term ?

d) Suggest a suitable name of this quadrilateral.​

Answer 1

Step-by-step explanation:

Let the four angles of a quadrilateral are

(a−3d)

∘

, (a−d)

∘

, (a+d)

∘

and (a+3d)

∘

∴a−3d+a−d+a+d+a+3d=360

∘

⟹a=90

∘

But the greatest angle is double the least, i.e.,

a+3d=2×(a−3d)=2a−6d

∴9d=2a−a=a=90

∘

∴d=

9

90

=10

∘

∴ Least angle a−3d=90

∘

−3×10

∘

=60

∘

=

3

π