Mattea was asked to find the measure of an interior angle of a regular octagon. Mattea’s work is shown below.

Steps
Mattea’s Work
Step 1
(n minus 2) 180 degrees = (9 minus 2) 180 degrees
Step 2
7 (180 degrees) = 1260 degrees
Step 3
1260 degrees divided by 8 = 157.5 degrees

Where, if at all, did Mattea first make a mistake finding the measure of an interior angle?
step 1
step 2
step 3
Mattea did not make a mistake.

141 3/7 degrees, Mattea did not make a mistake.

Step-by-step explanation:

Find each of the interior angles of the regular heptagon.  

The formula that gives the interior angle measure for a regular polygon with any number of sides is 180(n-2)/n where n is the number of sides.

So a regular heptagon's interior angle measures: 180(7-2)/7 = 128 4/7.  

Angle A and D would be 128 4/7 degrees.

Step 2: Find angle BAC. We know that a square's interior angle is 90 degrees and a heptagon's is 128 4/7 degrees. We will subtract those from 360 degrees to find angle BAC.

Angle BAC = 360 - (angle A + 90)

                  = 360 - (128 4/7 + 90)

                  = 360 - 218 4/7

                  = 141 3/7 degrees

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is