Hello, careness

Edit: I read my diagram incorrectly!

21. Given: .

Find Code:

A
*
θ
* *
* *
E o *
*2θ θ*
* o D
2θ
* *
180-3θ
* *
B o * * * o C

Draw segments

. . Let

Since is isosceles: .

is an exterior angle of

. . Hence: .

Since is isosceles: .

At point D, we have: .

. .

Since is isosceles: . .[1]

But is a base angle of an isosceles triangle with vertex angle

.Hence: . .[2]

Equate [2] and [1]: .

. .

is the central angle of a regular heptagon.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Consider this diagram . . . Code:

A
*
/θ\
/ \
/ \
/ \
/ \ D
/ *
/ * \
/ * \
/ * \
B * - - - - - - - - - *C

Given: .Isosceles triangle

. . . . . .

Then: . , the central angle of a regular pentagon.