Question

algebraic exterior angles
due mar 26, 2026 by 11:59pm points 100
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assignment overview 1
score: 0/8 penalty: 1 off
exterior angles of polygons
question
the measures of the exterior angles of a pentagon are ( 2x^{circ},3x^{circ},4x^{circ},6x^{circ} ), and ( 9x^{circ} ). solve for ( x ).
answer
attempt 1 out of 2
( x= )

Explanation:

Step1: Use the exterior angle sum property

The sum of exterior angles of any polygon is \(360^{\circ}\).
For the pentagon with exterior angles \(2x^{\circ},3x^{\circ},4x^{\circ},6x^{\circ},9x^{\circ}\), we have the equation \(2x + 3x+4x + 6x+9x=360\).

Step2: Combine like - terms

Combine the left - hand side terms: \((2 + 3+4 + 6+9)x=360\).
Since \(2+3 + 4+6+9=24\), the equation becomes \(24x = 360\).

Step3: Solve for \(x\)

Divide both sides of the equation \(24x = 360\) by \(24\): \(x=\frac{360}{24}\).
Simplify \(\frac{360}{24}=15\).

Answer:

\(x = 15\)