Question

algebraic exterior angles
due mar 26, 2026 by 11:59pm points 100
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assignment overview 1
score: 5/8 penalty: 1 off
exterior angles of polygons
question
the measures of the exterior angles of a heptagon are ( x ^ { circ }, 4 x ^ { circ }, 5 x ^ { circ }, 6 x ^ { circ }, 7 x ^ { circ }, 8 x ^ { circ } ), and ( 9 x ^ { circ } ). find the measure of the largest exterior angle.
answer
attempt 1 out of 2

Explanation:

Step1: Use the sum of exterior angles formula

The sum of the exterior angles of any polygon is \(360^{\circ}\).
So, \(x + 4x+5x + 6x+7x+8x + 9x=360\).
Combine like - terms: \((1 + 4+5 + 6+7+8 + 9)x=360\).
Calculate the coefficient: \(40x = 360\).

Step2: Solve for \(x\)

Divide both sides of the equation \(40x = 360\) by \(40\): \(x=\frac{360}{40}=9\).

Step3: Find the largest exterior angle

The largest exterior angle is \(9x\).
Substitute \(x = 9\) into \(9x\): \(9\times9 = 81\).

Answer:

\(81^{\circ}\)