in the diagram, ABCDEF is a regular hexagon and ABGH is a square
a) find angle ABC and angle CBG
b) find the angle of triangle ACG
Answers
Answer:
Given that ABCDEF is a regular hexagon, so all sides of it are equal in length.
Sum of the angles of a n− sided polygon =(n−2)×180
Hence,
Sum of all angles of a hexagon
=(6−2)×180
=720
And,
Each angle of a regular hexagon
=
6
720
=120.......(1)
Quadrilateral ABEF contains half the angle measure of the hexagon.
Hence, its interior angle measure
=720/2=360
∠AFE=120.......(ii) [ from (1)]
In △AFE,
AF=EF [ since, they are a part of regular hexagon].......(iii)
⇒∠FAE=∠FEA
[ Angles opposite to equal sides are equal]
In △AFE,
∠FAE+∠FEA+∠AFE=180
[ sum of all angles of a triangle is 180
o
]
substituting (ii) & (iii) in above equation,
∠FAE=∠FEA=30
o
∠FAE+∠EAB=120
o
[ Angle of a regular hexagon]
∴∠EAB=90
o
.......(iv)
∠ABE=1/2×120
o
[∵∠ABE bisects ∠ABC]
=60
o
In △ABE,
∠AEB+∠ABE+∠EBA=180
o
[ sum of all angles of a triangle]
∠AEB=180
o
−60
o
−90
o
=30
o
[ from (iv) & (v) ]
∠ABE=60
o
∠EAB=90
o
∠AEB=30
o
Step-by-step explanation:
I hope this figure would help you in understanding.
