# 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?

Feb 25, 2018

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

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

5t+ 30 – 25 + 30 + 56 + 66 – 14 = 360

$5 t = 360 - 143 = 217$

$t = \frac{217}{5} = 43.4$

-Sahar :)

Feb 25, 2018

$t = \frac{217}{5}$

#### Explanation:

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

$\text{sum the 6 exterior angles and equate to 360}$

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

$\Rightarrow 5 t + 143 = 360$

$\text{subtract 143 from both sides}$

$5 t \cancel{+ 143} \cancel{- 143} = 360 - 143$

$\Rightarrow 5 t = 217$

$\text{divide both sides by 5}$

$\frac{\cancel{5} t}{\cancel{5}} = \frac{217}{5}$

$\Rightarrow t = \frac{217}{5} \leftarrow \textcolor{red}{\text{exact value}}$