To find the sum of the interior angles of any polygon, use the formula $\displaystyle (n-2)\cdot 180$, where n represents the number of sides of a polygon.

In this case:

$\displaystyle (5-2)\cdot 180=540$

The sum of the interior angles will be 540. Go through each answer choice and see which one adds up to 540 (including the original angle given in the problem).

The only one that does is 120, 115, 95, 105 and the original angle of 105.

The sum of interior angles in a heptagon is $\displaystyle 900$ degrees. Note that to find the sum of interior angles of any polygon, it is given by the formula:

$\displaystyle (s-2)180$ degrees, where $\displaystyle s$ is the number of sides of the polygon.

Three interior angles (call them $\displaystyle b,c,d$)  are unknown, but we are told that the sum of them is equal to the sum of four other equivalent angles (which we'll designate $\displaystyle a$):

$\displaystyle 4a=b+c+d$

Further more, all of these angles must sum up to $\displaystyle 900$ degrees:

$\displaystyle 4a+b+c+d=900$

We may not be able to find $\displaystyle b$, $\displaystyle c$, or $\displaystyle d$, indvidually, but the problem does not call for that, and we need only use their relation to $\displaystyle a$, as stated in the first equation with them. Utilizing this in the second, we find:

$\displaystyle 4a+4a=900$

$\displaystyle a=\frac{900}{8}=112.5$

Always begin working through problems like this by filling in all available information. We know that we can fill in two of the angles, giving us the following figure:

Now, we know that for any polygon, the total number of degrees in the figure can be calculated by the equation:

$\displaystyle d = 180 *(s-2)$, where $\displaystyle s$ is the number of sides.

Thus, for our figure, we have:

$\displaystyle d = 180 * 3 = 540$

Based on this, we know:

$\displaystyle 540 = 110+50 - a + 135 + a + 50 + 2a$

Simplifying, we get:

$\displaystyle 540 = 345 + 2a$

Solving for $\displaystyle a$, we get:

$\displaystyle 195 = 2a$ or $\displaystyle a = 97.5$

To begin, recall that the total degrees in any figure can be calculated by:

$\displaystyle d = 180 * (s-2)$, where $\displaystyle s$ represents the total number of sides. Thus, we know for our figure that:

$\displaystyle d = 3*180 = 540$

Now, based on our figure, we can make the equation:

$\displaystyle a+2a+3a+120+80 = 540$

Simplifying, we get:

$\displaystyle 6a = 340$ or $\displaystyle a = 56.6666666666666....$

This means that $\displaystyle 3a$ is $\displaystyle 170$. Quantity A is larger.

The base of the triangle is 4 + 4 = 8 so the total perimeter is 5 + 5 + 8 = 18.

This Isosceles triangle has two sides with a length of $\displaystyle \small \frac{3}{9}$ foot and one side length that is half of the length of the two equivalent sides. 

To find the missing side, double the value of side $\displaystyle \small a$'s denominator:

$\displaystyle \small \frac{3}{9}=\frac{1}{3}$. Thus, half of $\displaystyle \small \frac{1}{3}=\frac{1}{6}$.

Therefore, this triangle has two sides with lengths of $\displaystyle \small \frac{1}{3}$ and one side length of $\displaystyle \small \frac{1}{6}$. 

To find the perimeter, apply the formula: 

$\displaystyle \small p=2a+b$

$\displaystyle \small p=\frac{1}{3}+\frac{1}{3}+\frac{1}{6}$

$\displaystyle \small p=\frac{2}{6}+\frac{2}{6}+\frac{1}{6}=\frac{5}{6}=\frac{10}{12}$ foot $\displaystyle \small = 10$ inches

To solve this problem apply the formula: $\displaystyle \small p=2a+b$.

However, first calculate the length of the missing side by: $\displaystyle \small 13\div2=6.5$.

Thus, the solution is:

$\displaystyle \small p=13+13+6.5=32.5$

To solve this problem apply the formula: $\displaystyle \small p=2a+b$.

However, first calculate the length of the missing side by:

$\displaystyle \small p=2(a)+12$

$\displaystyle \small a=12\times5=60$

$\displaystyle \small p=2(60)+12$

$\displaystyle \small p=120+12=132$

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that $\displaystyle b=\frac{3}{4}$ ft and that the sides with length $\displaystyle a$ are half the length of side $\displaystyle b$, find the length of $\displaystyle a$ by: $\displaystyle \frac{3}{4}=\frac{6}{8}$ and half of $\displaystyle \frac{6}{8}=\frac{3}{8}$. Thus, both of sides with length $\displaystyle a$ must equal $\displaystyle \frac{3}{8}$ ft. 

Now, apply the formula: $\displaystyle p=2a+b$.

$\displaystyle p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}$

Then, simplify the fraction/convert to mixed number fraction:


$\displaystyle \frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$
 

In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\displaystyle \small p=2a+b$

Each of the missing sides equal: 

$\displaystyle \small a=\frac{7}{3}\times4=\frac{28}{3}$ 

Then apply the perimeter formula:
$\displaystyle \small p=\frac{28}{3}+\frac{28}{3}+\frac{7}{3}=\frac{63}{3}=21$