C A hexagon ABCDEF is shown.
115°
D
B
145°
Angle CDE is twice the size of angle DEF.
E
Work out the size of angle CDE.
You must show all your working.
160°
F
Total marks: 5

since the sum of interior angles of hexagon is 720 °

you add the known angles

ie 115 +90+145+160

you get 510

subtract it from 720

you get 210

divide 210 by 3

you get 70

angle cde is 140

∠ CDE = 140°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

let ∠ DEF be x then ∠ CDE = 2x

sum the interior angles and equate to 720

160 + 90 + 145 + 115 + 2x + x = 720 , that is

510 + 3x = 720 ( subtract 510 from both sides )

3x = 210 ( divide both sides by 3 )

x = 70

Then

∠ CDE = 2x = 2 × 70 = 140°

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225