Answer:
The angles have measurements 36, 72, 108, 144, and 180.
Step-by-step explanation:
Pentagon has 5 sides and 5 angles.
The amount of triangles formed by choosing one vertex and drawing from that vertex to every nonadjacent vertex is 3.
3(180)=540 which is the sum of the angles in a pentagon.
So since the ratio is 1:2:3:4:5, that means the angles are 1x,2x,3x,4x, and 5x.
We have the equation 1x+2x+3x+4x+5x=540 to solve.
15x=540
Divide 15 on both sides:
x=540/15
x=36
1x=36
2x=72
3x=108
4x=144
5x=180
The angles have measurements 36, 72, 108, 144, and 180.
