Question

the sum of the interior angles of a polygon with n sides is
select one:
a. 360
b. 180
c. $180(n-2)$

the sum of the interior angles of a quadrilateral ___ the sum of its exterior angles.
select one:
a. equals
b. >
c. <

Explanation:

Step1: Recall polygon interior angle formula

The standard formula for the sum of interior angles of an n-sided polygon is derived by dividing the polygon into (n-2) triangles, each with an angle sum of 180°.
Expression: $\text{Sum of interior angles} = 180(n-2)$

Step2: Calculate quadrilateral interior angle sum

For a quadrilateral, $n=4$. Substitute into the formula:
Expression: $180(4-2) = 360^\circ$

Step3: Recall quadrilateral exterior angle sum

The sum of exterior angles of any convex polygon is always $360^\circ$.
Expression: $\text{Sum of exterior angles} = 360^\circ$

Step4: Compare the two sums

Compare the interior and exterior angle sums of the quadrilateral:
Expression: $360^\circ = 360^\circ$

Answer:

1. c. 180(n-2)
2. a. equals