Question

quiz #3
show all work and include units to receive full credit! circle your answers.

1. simplify the expression.

(-7x² - 8) - (-2 + 6x² + 6x)=
are these like terms?
-7x²+6x² + 6x=
-8 + 2=-10

1. find the measure of one angle of a 13 - sided regular polygon.

Explanation:

Step1: Remove parentheses

\[

$$\begin{align*} (-7x^{2}-8)-(-2 + 6x^{2}+6x)&=-7x^{2}-8 + 2-6x^{2}-6x\\ \end{align*}$$

\]

Step2: Combine like - terms

\[

$$\begin{align*} &(-7x^{2}-6x^{2})-6x+(-8 + 2)\\ &=-13x^{2}-6x - 6 \end{align*}$$

\]

Step1: Use the formula for the sum of interior angles of a polygon

The sum of interior angles of an \(n\) - sided polygon is \(S=(n - 2)\times180^{\circ}\), where \(n = 13\). So \(S=(13 - 2)\times180^{\circ}=11\times180^{\circ}=1980^{\circ}\).

Step2: Find the measure of one angle

Since the polygon is regular, all angles are equal. So the measure of one angle \(A=\frac{S}{n}=\frac{1980^{\circ}}{13}\approx152.31^{\circ}\)

Answer:

\(-13x^{2}-6x - 6\)