Question

The diagram shows a convex polygon.

1410
2y
у
140°
1390
What is the value of y?
O
y =

Answer 1

`\textit{sum of all interior angles in a polygon}\\\\ S=180(n-2) \begin{cases} n = \stackrel{\textit{number of}}{\textit{sides}}\\[-0.5em] \hrulefill\\ n = 5 \end{cases}\implies S = 180(5 - 2)\implies S = 540 \\\\[-0.35em] ~\dotfill\\\\ y+141+2y+140+139=540\implies 3y+420=540 \\\\\\ 3y=120\implies y = \cfrac{120}{3}\implies \boxed{y = 40}`