Question

1. the sum of the measures of the interior angles of a convex polygon with r sides is 180(r - 2) degrees. what is the sum of the measures of the interior angles of a convex polygon with 10 sides? f. 900° g. 1,440° h. 1,798° j. 1,800° k. 2,160° 3. in the standard (x,y) coordinate plane, point a has coordinates (-8,-3). point a is translated 8 units to the right and 3 units up, and that image is labeled a. what are the coordinates of a? a. (-16, -6) b. (-11,-11) c. (-8, -6) d. (0, 0) e. (16, 6)

Explanation:

1.

Step1: Identify the formula and value of \(r\)

The formula for the sum of interior - angles of a convex polygon is \(S = 180(r - 2)\), and \(r = 10\).

Step2: Substitute \(r\) into the formula

\[

$$\begin{align*} S&=180\times(10 - 2)\\ &=180\times8\\ & = 1440^{\circ} \end{align*}$$

\]

Step1: Recall the rules of translation

For a translation of \(a\) units to the right and \(b\) units up, the new \(x\) - coordinate is \(x_{new}=x_{old}+a\) and the new \(y\) - coordinate is \(y_{new}=y_{old}+b\). Here, \(x_{old}=-8\), \(y_{old}=-3\), \(a = 8\), and \(b = 3\).

Step2: Calculate the new \(x\) - coordinate

\(x_{new}=-8 + 8=0\)

Step3: Calculate the new \(y\) - coordinate

\(y_{new}=-3+3 = 0\)

Answer:

G. \(1440^{\circ}\)

2.