A hexagon ABCDEF is shown.
С-115
D
B
145
Angle CDE is twice the size of angle DEF.
Work out the size of angle CDE.
You must show all your working.
E
160°
+
F


Sagot :

Answer:

140

Step-by-step explanation:

115+165+140+90=510

180*4=720 (sum of interior angles of hexagon)

115+165+140+90+x+2x=720

why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x

510+2x+x=720

3x=210

x=210/3

x=70

ANGLE DEF IS 70

so  because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140

ANGLE CDE =140

The angle CDE is 140°.

What is a hexagon?

A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.

According to the given problem,

We know,

Sum of the interior angles of a polygon is,

Sum = 180° (n - 2) where n is the number of sides,

Here n = 6 , then

Sum = 180° × 4 = 720°

Let ∠ DEF be x  

Therefore ∠ CDE = 2x,

Sum the interior angles,

⇒ 160 + 90 + 145 + 115 + 2x + x = 720

⇒ 510 + 3x = 720 ( subtracting 510 from both sides )

⇒ 3x = 210 ( dividing both sides by 3 )

⇒ x = 70

∠ CDE = 2x

           = 2 × 70

           = 140°

Hence, we can conclude, in the hexagon, the angle CDE is 140°.

Learn more about hexagon here:

https://brainly.com/question/2001860

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