Question 182
A regular pentagon ABCDE and a square ABFG are formed on opposite sides of AB. Find ∠BCF?
Open in App
Solution
Given, ABCDE is a regular pentagon.
Then, measure of each interior angle of the regular pentagon =SumofinterioranglesNumberofsides=(x−2)×180∘5=(5−2)×180∘5=540∘5=108∘∴∠CBA=108∘
Join CF.
Now, ∠FBC=360∘−(90∘+108∘)=360∘−198∘=162∘
In ΔFBC, by the angle sum property, we have ∠FBC+∠BCF+∠BFC=180∘⇒∠BCF+∠BFC=180∘−162∘⇒∠BCF+∠BFC=18∘
Since, ΔFBC is an isosceles triangle and BF = BC. ∴∠BCF=∠BFC=9∘