Question

ABCDE is aregular pentangon
X=?

Answer 1

x = 5.2

Explanation:

Measure of interior angle of a regular polygon =
`((n-2)*180)/(n)`

Here n = number of sides of the polygon

Interior angle of a regular pentagon =
`((5-2)*180)/(5)`

= 108°

By applying cosine rule in ΔABK,

(BK)² = (AK)² + (AB)² - 2(AK)(AB)cos(108)°

(x + 3)² = 4² + 6² - 2(4)(6)cos(108)°

x² + 6x + 9 = 16 + 36 - (-14.83)

x² + 6x = 57.83

x² + 6x - 57.83 = 0

x =
`(-6\pm √(6^2-4(1)(-57.83)))/(2(1))`

x =
`(-6\pm16.35)/(2)`

x ≈ -11.2, 5.2

Since, x can't be negative,

x = 5.2 will be the answer.