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The exterior angles of a quadrilateral have measures of 72∘, 58∘, 2x∘, and 3x∘. How do I find the value of x?

1 Answer

The Lonely Donut · Stefan V.

Feb 12, 2017

$x = 46$ $x = 46$

The sum of all exterior angles of any polygon is always $360$ $360$ degrees.

Explanation:

In any given polygon, whether there are $3$ $3$ sides or $16$ $16$ sides, the sum of all exterior angles is always $360^{\circ}$ $360^@$ .

Therefore, your equation would be

$72^{\circ} + 58^{\circ} + {(2 x)}^{\circ} + {(3 x)}^{\circ} = 360^{\circ}$ $72^@ + 58^@ + (2x)^@ + (3x)^@ = 360^@$

Simplify to get the answer.

$72 + 58 + 2 x + 3 x = 360$ $72 + 58 + 2x + 3x = 360$

$130 + 5 x = 360$ $130 + 5x = 360$

$5 x = 230$ $5x = 230$

$x = 46$ $x = 46$

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