Question

Find the measure of ∠NED, not ∠CED.

Answer 1

`m\angle NED = 100\degree`

`m\angle CED = 80\degree`

Explanation:

By exterior angle theorem:

(9x - 8)° = (5x - 10)° + 50°

(9x - 8)° = (5x - 10 + 50)°

(9x - 8)° = (5x + 40)°

9x - 8 = 5x + 40

9x - 5x = 40 + 8

4x = 48

x = 48/4

x = 12

(9x - 8)° = (9*12 - 8)° = (108 - 8)° = 100°

`\implies m\angle NED = 100\degree`

`m\angle CED = 180\degree - 100\degree` (Linear pair angles)

`\therefore m\angle CED = 80\degree`

Answer 2

`\huge{ \mathcal{  \underline{ Answer }}}\:  ✓`

Measure of Exterior Angle of a triangle is equal to the sum of measures of two opposite interior angles .

From above statement we have :

• 
  `9x - 8 = 5x - 10 + 50`

• 
  `9x - 5 x = 40 + 8`

• 
  `4x = 48`

• 
  `x = (48)/(4)`

• 
  `x = 12`

_____________________________

`\mathrm{\angle \: NED = 9x - 8}`

• 
  `(9 * 12) - 8`

• 
  `108 - 8`

• 
  `100°`

_____________________________

`\mathrm{ \#TeeNForeveR}`