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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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