The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles. How many sides does this polygon have?

6 sides

Step-by-step explanation:

The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles. How many sides does this polygon have?

Let us represent:

Sum of Exterior angle as x

Sum of Interior angle as y

Note that:

The sum of the exterior angles of a polygon = 180 - The sum of the interior angles

Hence,

The sum of the exterior angles of a polygon + The sum of the interior angles = 180

x + y = 180

The measure of one interior angle of a regular polygon is two times the measure of one of its exterior angles.

2x = y

Substituting

x + 2x = 180°

3x = 180°

x = 180/3

x = 60°

Solving for y

2x = y

2 × 60° = y

120° = y

Hence,

Sum of Exterior angle as x = 60°

Sum of Interior angle as y = 120°

The number of sides of a polygon is

360°÷ Sum of Exterior angles

= 360° ÷ 60

= 6 sides

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3