Find the sum of the degree measures of the interior angles of (i) a hexagon (ii) an octagon (iii) a decagon.
Answers
Answer:
360°
Step-by-step explanation:
(i) Hexagon
Numbers of sides, n=6
Sum of the interior angles =(2n–4)90
0
=((2×6)–4)×90
0
=(12–4)90
0
=8×90
0
=720
0
Sum of the exterior angles =360
0
.
(ii) Octagon
Numbers of sides, n=8
Sum of the interior angles =(2n–4)90
0
=((2×8)–4)×90
0
=(16–4)90
0
=12×90
0
=1080
0
Sum of the exterior angles =360
0
.
(iii) Pentagon
Numbers of sides, n=5
Sum of the interior angles =(2n–4)90
0
=((2×5)–4)×90
0
=(10–4)90
0
=6×90
0
=540
0
Sum of the exterior angles =360
0
.
(iv) Nonagon
Numbers of sides, n=9
Sum of the interior angles =(2n–4)90
0
=((2×9)–4)×90
0
=(18–4)90
0
=14×90
0
=1260
0
Sum of the exterior angles =360
0
.
(v) Decagon
Numbers of sides, n=10
Sum of the interior angles =(2n–4)90
0
=((2×10)–4)×90
0
=(20–4)90
0
=16×90
0
=1440
0
Sum of the exterior angles =360
0
.