The ratio of the angle measures of a pentagon is 4:5:3:8:7. What is the measure of the smallest angle?
60
The sum of the interior angles of a pentagon is 180(5-2) = 540º
so
4x + 5x + 3x + 8x + 7x = 540
solve for x and sub into 3x
To find the measure of the smallest angle in a pentagon with the given ratio of angle measures, we need to determine the value of the smallest angle compared to the other angles.
Step 1: Add up the ratio values.
4 + 5 + 3 + 8 + 7 = 27
Step 2: Determine the value of one ratio unit.
Since the total ratio is 27, we divide 360 degrees (the total number of degrees in a pentagon) by 27.
360 ÷ 27 ≈ 13.33
Step 3: Find the measure of the smallest angle.
Multiply the value of one ratio unit by the given smallest ratio, which is 4.
13.33 * 4 = 53.33
The measure of the smallest angle in the pentagon is approximately 53.33 degrees.