What is the measure of an angle, in degrees, if its supplement is six times its complement?

72 degrees.

Step-by-step explanation:

We can name the measure of the angle x.

We can name the measure of the complement of it y.

Note that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees.

Using this info, we can set up two equations.

x+y=90

x+6y=180

Subtract the first equation from the second to eliminate x. You can do both ways, but I prefer to keep the equation positive.

x+6y=180

-x -y   -90

5y=90

Divide both sides by 5.

y=18

The complement is 18, now we can plug that in to find x.

x+18=90

Subtract 18 from both sides.

x=72

The measure of the angle is 72 degrees.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.