A convex quadrilateral has exterior angle measures, one at each vertex, of 5b+7°, 34b–33°, b+36°, and 37b–35°. What is the value of b?

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A convex quadrilateral has exterior angle measures, one at each vertex, of 5b+7°, 34b–33°, b+36°, and 37b–35°. What is the value of b?

2 Answers

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Answer 1 · 2018-02-25T18:52:49

$b=5$

Explanation:

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

$"the sum of the 4 exterior angles is then"$

$5b+7+34b-33+b+36+37b-35=360$

$rArr77b-25=360$

$"add 25 to both sides"$

$77bcancel(-25)cancel(+25)=360+25$

$rArr77b=385$

$"divide both sides by 77"$

$(cancel(77) b)/cancel(77)=385/77$

$rArrb=5$

Answer 2 · 2018-02-25T18:56:44

$b = 5^@$ .

Explanation:

As soon as I read the question and it was talking about exterior angles I wrote the values above are equal to $360^@$ .

$5b+7 + 34b - 33 + b + 36 + 37b - 35 = 360^@$

It equals $360^@$ as exterior angles add up to $360^@$ as it goes all around a point. So when you simplify the values give you get

$77b - 25 = 360$

$77b = 360 + 25$

$77b= 385$

Divide both sides by $77$ to isolate $b$

$b= 5$

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A convex quadrilateral has exterior angle measures, one at each vertex, of 5b+7°, 34b–33°, b+36°, and 37b–35°. What is the value of b?

2 Answers

Explanation:

Explanation:

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