Question

Question #1
Solve for x
E
16x9
D
C
45°

Answer 1

`x = (3\pi)/(64) +(9)/(16)`

Explanation:

We have

∠D = 45° = 45* π/180 radians = π/4 radians - eq(1)

big arc + small arc = 2π

small arc = 16x - 9

⇒ big arc = 2π - small arc

big arc = 2π - 16x + 9

`\angle D = (big \;arc - small \;arc)/(2)`

`\angle D = (2\pi - 16x + 9 - 16x +9)/(2)\\\\= \angle D = (2\pi - 32x + 19 )/(2)\\\\\angle D = \pi - 16x + 9`

Equating with eq(1)

π - 16x + 9 = π/4

⇒ 16 x = π - (π/4) +9

⇒ 16 x = (3π/4) +9

⇒
`x = (1)/(16) ((3\pi)/(4) +9)`

`x = (3\pi)/(64) +(9)/(16)`