Question

(SAT Prep) Find the value of x in each of the following exercises:

Answer 1

Answer:

$x=115^o$

Step-by-step explanation:

Angles Inside a Polygon

A polygon of n sides must have the sum of its internal angles  

$S=180^o(n-2)$

The polygon shown in the figure has n=5 sides, so the sum of its internal angles is

$S=180^o(5-2)=540^o$

The construction of the internal angles of the polygon is shown in the image below. The sum of them is

$50+180-x+180-x+360-x+x=540$

Reducing

$-2x+770=540$

Solving

$\displaystyle x=\frac{770-540}{2}$

$\boxed{x=115^o}$