# 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?

Feb 25, 2018

$b = 5$

#### Explanation:

$\text{the " color(blue)"sum of the exterior angles } = {360}^{\circ}$

$\text{the sum of the 4 exterior angles is then}$

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

$\Rightarrow 77 b - 25 = 360$

$\text{add 25 to both sides}$

$77 b \cancel{- 25} \cancel{+ 25} = 360 + 25$

$\Rightarrow 77 b = 385$

$\text{divide both sides by 77}$

$\frac{\cancel{77} b}{\cancel{77}} = \frac{385}{77}$

$\Rightarrow b = 5$

Feb 25, 2018

$b = {5}^{\circ}$.

#### Explanation:

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

$5 b + 7 + 34 b - 33 + b + 36 + 37 b - 35 = {360}^{\circ}$

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

$77 b - 25 = 360$

$77 b = 360 + 25$

$77 b = 385$

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

$b = 5$