If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
Practice Questions
1 question
Q1
If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
135 degrees
120 degrees
108 degrees
150 degrees
The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.
Questions & Step-by-step Solutions
1 item
Q
Q: If a polygon has 8 sides, what is the measure of each interior angle in a regular octagon?
Solution: The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) * 180] / n. For an octagon (n=8), it is [(8-2) * 180] / 8 = 135 degrees.
Steps: 7
Step 1: Identify the number of sides in the polygon. For an octagon, n = 8.
Step 2: Use the formula for calculating the measure of each interior angle of a regular polygon: [(n-2) * 180] / n.
Step 3: Substitute the value of n into the formula: [(8-2) * 180] / 8.
Step 4: Calculate (8-2) which equals 6.
Step 5: Multiply 6 by 180 to get 1080.
Step 6: Divide 1080 by 8 to find the measure of each interior angle: 1080 / 8 = 135.
Step 7: Conclude that each interior angle in a regular octagon measures 135 degrees.
