Respuesta :

discipulus

Answer:

[tex]40 \degree + 107\degree + x\degree = 180\degree \\ x\degree = 180\degree - 147\degree \\ x\degree = 33\degree \\ 33\degree + 65\degree + y\degree = 180\degree \\ y\degree = 180\degree - 98\degree \\ y\degree = 82\degree[/tex]

SalmonWorldTopper

[tex]\large\underline{\sf{Solution-}}[/tex]

In triangle ADC

  • ∠DAC = 40°

  • ∠ADC = 107°

  • ∠ACD = x°

Now,

We know that, Sum of all interior angles of a triangle is supplementary.

Thus,

∠ADC + ∠DAC + ∠ACD = 180°

⇛ 40° + 107° + x° = 280°

⇛ 147° + x = 180°

⇛ x = 33°

[tex] \\ \rm\implies \:\boxed{\tt{ \angle \: ACD \: = \: 33 \degree \: }} \\ [/tex]

Now, ACE is a line.

So,

∠ACD + ∠DCB + ∠BCE = 180°

⇛ x + 65° + y = 180°

⇛ 33° + 65° + y = 180°

⇛ 98° + y = 180°

⇛ y = 180° - 98°

⇛ y = 82°

[tex] \\ \rm\implies \:\boxed{\tt{ y \: = \: 82 \degree \: }} \\ [/tex]

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