Practice30 Create account

Two regular polygons have their numbers of sides in the ratio 1 : 2, and their interior angles in the ratio 3 : 4. How many sides do they have?

Competition practiceGeometry

A5 and 10
B4 and 8
C6 and 12
D3 and 6

Step-by-Step Solution

With

n

and

2 n

sides:

\frac{( n - 2 ) / n}{( 2 n - 2 ) / ( 2 n )} = \frac{3}{4}

, i.e.

\frac{2 ( n - 2 )}{2 n - 2} = \frac{3}{4}

. So

8 n - 16 = 6 n - 6

and

n = 5

. Check: 108° : 144° = 3 : 4.

Answer: A) 5 and 10

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Geometry practice questions

More Geometry practice

Each interior angle of a regular polygon is five times each exterior angle. How many…What is the area of a regular octagon with sides of 2 cm?A regular hexagon is inscribed in a circle of radius 7 cm. What is the perimeter of the…A regular 12-sided polygon is inscribed in a circle of radius 5 cm. What is its area?At most how many interior angles of a convex polygon can be acute?