If the exterior angles of a pentagon are in the ratio 1:2:3:4:5.Find all the interior angles of the pentagon
Answers
Step-by-step explanation:
Given ratio is 1: 2 : 3: 4: 5.
Let the exterior angles of a pentagon are in the ratio 1x,2x,3x,4x,5x.
We know that sum of exterior angles of a pentagon = 360.
1x + 2x + 3x + 4x + 5x = 360
15x = 360
x = 360/15
x = 24.
The exterior angles of the Pentagon are 24, 2(24),3(24),4(24),5(24)
= 24,48,72,96,120.
We know that sum of interior angles of a Pentagon = 180.
180 - 24, 180 - 48,180 - 72,180 - 96,180 - 120.
= 156,132,108,84,60.
Therefore the interior angles of a Pentagon are 156,132,108,84,60.
Hope this helps!!
Answer:
156,132,108,84,60
Step-by-step explanation:
The sum of exterior angles = 360
Let each exterior angles is x,2x,3x,4x,5x
x+2x+3x+4x+5x = 360
15x = 360
x =24
and interior angle+exterior angle (that are
adjacent angle each other)=180
so interior angle 1 (adjacent with x) is 180-24 = 156
interior angle 2 (adjacent with 2x) is 180-2*24 = 132
interior angle 3 (adjacent with 3x) is 180-3*24 = 108
interior angle 4 (adjacent with 4x) is 180-4*24 = 84
interior angle 5 (adjacent with 5x) is 180-5*24 = 60