Question

1. 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 is the measure of the angle formed by two consecutive walls of the tribune. la tribuna 135 8m = c8 - 2*180 8n=180n - 360 -180 -160 -112 -170 5x = 170/370 = 74

Explanation:

Step1: Recall the formula for the measure of an interior angle of a regular polygon.

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \). For a regular octagon, \( n = 8 \).

Step2: Substitute \( n = 8 \) into the formula.

Substitute \( n = 8 \) into \( \frac{(n - 2)\times180^{\circ}}{n} \), we get \( \frac{(8 - 2)\times180^{\circ}}{8} \).

Step3: Calculate the numerator first.

Calculate \( (8 - 2)\times180^{\circ}=6\times180^{\circ} = 1080^{\circ} \).

Step4: Divide the numerator by the denominator.

Now divide \( 1080^{\circ} \) by \( 8 \): \( \frac{1080^{\circ}}{8}=135^{\circ} \).

Answer:

The measure of the angle formed by two consecutive walls (interior angle) of the regular octagonal room is \( 135^{\circ} \).