Question

ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room built by Buontalenti called the Tribune (La Tribuna in Italian). This room is shaped like a regular octagon. What angle do consecutive walls of the Tribune make with each other?

Answer 1

Given :- ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room built by Buontalenti called the Tribune (La Tribuna in Italian). This room is shaped like a regular octagon. What angle do consecutive walls of the Tribune make with each other?

Answer :-

we know that,

• Interior angles of a regular polygon = (n - 2) * 180° /n .
• Octagon = 8 sides .

so,

→ n = 8

then,

→ Measure of each angle = (8 - 2) * 180° / 8 = 6 * 180°/ 8 = 1080/8 = 135° (Ans.)

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Answer 2

Given :  ARCHITECTURE In the Uffizi gallery in Florence, Italy, there is a room built by Buontalenti called the Tribune (La Tribuna in Italian).

This room is shaped like a regular octagon.

To Find : What angle do consecutive walls of the Tribune make with each other

Solution:

regular octagon.  has all  8 sides equal and all  8 interior angles equal .

interior angle of polygon is given by  ( n- 2) * 180° / n

where n is number of sides

n = 8  as its octagon

angle consecutive walls of the tribune make with each other

=  ( 8- 2) * 180° /8

= 6 * 180° /8

= 3 * 180° /4

= 3 * 45°

= 135°

angle consecutive walls of the tribune make with each other  = 135°

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