Question

A heptagon has angles that measure 100°, 160°, 120°, 115°, 140°, 120°, and n. What is n?

Answer 1

145∘

Explanation:

The sum of the interior angles of a heptagon (a seven-sided polygon) is given by the formula:

Sum of interior angles = (n − 2) × 180∘

where n is the number of sides (in this case, n = 7 for a heptagon).

Therefore, for a heptagon:

Sum of interior angles = (7 − 2) × 180∘ = 5 × 180∘ = 900∘

Now, you're given the measures of six angles: 100°, 160°, 120°, 115°, 140°, and 120°. Add these angles:

100 + 160 + 120 + 115 + 140 + 120 = 755∘

To find the measure of the seventh angle (n), subtract the sum of the given angles from the total sum of interior angles:

n = 900 − 755 = 145∘

Therefore, the measure of the seventh angle (n) is 145∘.