Sign In
The sum S of the interior angle measures of a polygon with n sides is given by the formula S=(n-2)180^(∘).
x=77
We are given a polygon and asked to find the value of x.
To do so, let's first recall the Interior Angle Measures of a Polygon Theorem.
|
Interior Angle Measures of a Polygon Theorem |
|
The sum S of the interior angle measures of a polygon with n sides is equal to the product of (n-2) and 180^(∘). S=(n-2) 180^(∘) |
The given polygon has 4 sides. We can substitute this number for n in the formula to find the sum of the measures of the interior angles of the polygon.
n= 4
Subtract term
Multiply
The sum of the angle measures of the given polygon is 360^(∘). Next, we can write an equation that sets S equal to the sum of the angle measures. S= Sum of the angle measures ⇓ 360^(∘)= 60^(∘)+ 128^(∘)+ 95^(∘)+ x^(∘) Finally, we can solve this equation for x. For simplicity, we will remove the degree symbol while solving.