Question

a regular pentagon ABCDE and a square ABFG are formed and opposite sides of AB . Find angle BCF

Answer 1

Answer:

<BCF = 9°

Step-by-step explanation:

In the figure attached with this answer,

ABCDE is a regular pentagon and ABFG is a square.

So the sides of pentagon and square are equal.

Each angle of square = 90°

Each angle of regular pentagon = 108°

From the figure <FBC =360 - [<ABF + <ABC]

<FBC = 360 - (90 +108 ) =360 - 198 = 162°

<BFC = <BCF  (since BF = BC, Δ BCF isosceles triangle )

<BCF= 1/2(180 - 162) =9°

Answer 2

Answer:

Ans is. 9

Step-by-step explanation:

in the figure ABCDE is a regular polygon and ABFG is a square

so, the sides of pentagon are equal = sides of square

each angle of square = 90°

each angle of regular Pentagon

5x = 180 + 360°

5x = 540°

x = 540°/5 = 108

from the figure

angle FBC = 360° ( angle ABF + angle ABC )

= 360° -- 198°

= 162°

angle BFC = angle BCF

( since BF = BC , ∆ BCF is isosceles ∆ )

angle BCF = 1/2 ( 180 -- 162 ) = 18°/2

9° ans