A convex hexagon has exterior angle measures, one at each vertex, of 30°, 2t–25°, 30°, 56°, 66°, and 3t–14°. What is the value of t?

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A convex hexagon has exterior angle measures, one at each vertex, of 30°, 2t–25°, 30°, 56°, 66°, and 3t–14°. What is the value of t?

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Answer 1 · 2018-02-25T17:59:30

Sum of exterior angle for any polygon is always $360^{\circ}$ $360^@$

$30°+ 2t–25°+ 30°+ 56°+ 66°+ 3t–14° = 360$

$5t+ 30 – 25 + 30 + 56 + 66 – 14 = 360$

$5t = 360-143=217$

$t=217/5 = 43.4$

-Sahar :)

Answer 2 · 2018-02-25T19:14:36

$t=217/5$

Explanation:

$"the "color(blue)"sum of the exterior angles "=360^@$

$"sum the 6 exterior angles and equate to 360"$

$30+2t-25+30+56+66+3t-14=360$

$rArr5t+143=360$

$"subtract 143 from both sides"$

$5tcancel(+143)cancel(-143)=360-143$

$rArr5t=217$

$"divide both sides by 5"$

$(cancel(5) t)/cancel(5)=217/5$

$rArrt=217/5larrcolor(red)"exact value"$

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A convex hexagon has exterior angle measures, one at each vertex, of 30°, 2t–25°, 30°, 56°, 66°, and 3t–14°. What is the value of t?

2 Answers

Explanation:

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