11. ABCDEFG is a regular heptagon. If AB and DC are
produced to meet at H, find the value of BHC.
Answers
Given : ABCDEFG is a regular heptagon. If AB and DC are produced to meet at H,
To find : value of ∠BHC.
Solution:
ABCDEFG is a regular heptagon.
Heptagon has 7 sides
internal angle = (n - 2) * 180°/n
= (7 - 2) * 180°/ 7
= 900°/7
∠ABC = ∠BCD = 900°/7
AB and DC are produced to meet at H,
Now in ΔBHC
∠ABC & ∠BCD are exterior angles
∠ABC = ∠BHC + ∠BCH
∠BCD = ∠BHC + ∠CBH
Adding both
=> ∠ABC + ∠BCD = ∠BHC + ∠BCH + ∠BHC + ∠CBH
=> 900°/7 + 900°/7 = ∠BHC + 180°
=> ∠BHC = 540°/7
=> ∠BHC = 77.14°
∠BHC = 77.14° = 540°/7 or 3π/7
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Answer:
angle BHC=77.1°
Step-by-step explanation:
value of BHC.
ABCDEFG is a regular heptagon.
Heptagon has 7 sides
Internal angle = (n - 2) * 180°/n
= (7 - 2) * 180°/ 7
= 900°/7
∠ABC = ∠BCD = 900°/7
AB and DC are produced to meet at H,
Now in ΔBHC
∠ABC & ∠BCD are exterior angles
∠ABC = ∠BHC + ∠BCH
∠BCD = ∠BHC + ∠CBH
Adding both
=> ∠ABC + ∠BCD = ∠BHC + ∠BCH + ∠BHC + ∠CBH
=> 900°/7 + 900°/7 = ∠BHC + 180°
=> ∠BHC = 540°/7
=> ∠BHC = 77.1°(after round off)
