Question

A regular pentagon has a perimeter of 60 cm.

Answer 1

Answer: $\angle CBD$= 36° CD= 6, BC= 8.258 cm and BD=10.20cm

Explanation:  Since, the total central angle of pentagon =360°

Thus,  $\angle DBA$=360°/5= 72 ( because pentagon made by the 5 equal triangles.

Since, BC bisects $\angle DBA$ therefore $\angle CBD$= $\angle DBA/2$= 72°/2=36°

b) Since, AD makes 1/5 of the total perimeter of the pentagon, therefore, AD=60/5=12

And,C is the midpoint of AD⇒ CD=AD/2=12/2=6

c) In $\triangle CBD$,     tan36°=CD/BC⇒BC=CD/tan36°=8.25829152289≈8.258 cm

 e) Again in $\triangle CBD$ ,

Sin36°=CD/BD⇒ BD=6/0.58778525229=10.2078097003≈10.20

Answer 2

A) ∠CBD is 1/10 the measure of the circle, 36°.

b) CD is 1/10 the perimeter, 6 cm.

c) CD/BC = tan(∠CBD)

d) BC = CD/tan(∠CBD) = (6 cm)/tan(36°) ≈ 8.258 cm

e) BD = (6 cm)/sin(36°) ≈ 10.208 cm