Lanice1
contestada

Find the measure of each interior angle
Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90

Respuesta :

[tex]\bf \textit{sum of all interior angles of a polygon}\\\\ 180(n-2)\quad \begin{cases} n=\textit{number of sides}\\ ---------\\ n=10 \end{cases}\implies 180(10-2)\implies 1440\\\\ -------------------------------\\\\ \begin{array}{lclll} &x + 5\\&x + 10\\&x + 20\\&x + 30\\&x + 35\\&x + 40\\&x + 60\\&x + 70\\&x + 80\\+&x + 90\\ &----\\ &10x+440 \end{array}\implies \begin{array}{llll} 10x+440=1440 \\\\\\ 10x=1000 \\\\\\ x=\cfrac{1000}{10}\implies x=100 \end{array}[/tex]

so.. to get every angle, simply plug in 10 for "x" for each.

Otras preguntas