Advertisements
Advertisements
Question
In the given figure, AB is the side of regular pentagon and BC is the side of regular hexagon. Angle APC is:
Options
132°
66°
90°
120°
MCQ
Advertisements
Solution
66°
Explanation:
Since,
AB is the side of regular pentagon.
∴ ∠AOB = `(360°)/5` = 72°
BC is the side of regular hexagon.
∴ ∠BOC = `(360°)/6` = 60°
From figure,
∠AOC = ∠AOB + ∠BOC = 72° + 60° = 132°
We know that,
The angle which an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circumference.
⇒ ∠AOC = 2∠APC
⇒ ∠APC = `(∠AOC)/2 = (132°)/2` = 66°
shaalaa.com
Is there an error in this question or solution?
