Question

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?

Answer 1

`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

`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`