Question

In ΔCDE, m ∠ C = ( x − 4 ) ∘ m∠C=(x−4) ∘ , m ∠ D = ( 9 x + 4 ) ∘ m∠D=(9x+4) ∘ , and m ∠ E = ( 2 x + 12 ) ∘ m∠E=(2x+12) ∘ . Find m ∠ D . m∠D.

Answer 1

`\bold{130^\circ}`

Explanation:

Given that:

In a
`\triangle CDE`:

`m\angle C = (x-4)^\circ\\m\angle D = (9x+4)^\circ\\m\angle E = (2x+12)^\circ`

To find:

`m\angle D = ?`

Solution:

We know that sum of internal angles of a triangle is equal to
`180^\circ`.

Here, we are given a
`\triangle CDE` and all its three internal angles.

Putting the sum of all three equal to
`180^\circ`.

`\angle C +\angle D +\angle E =180^\circ\\\Rightarrow (x-4)+(9x+4)+(2x+2)=180^\circ\\\Rightarrow 12x+12=180^\circ\\\Rightarrow x +1=15^\circ\\\Rightarrow x =14^\circ`

Putting value of
`x` in
`m\angle D =(9x+4)^\circ`

`\Rightarrow m\angle D = 9* 14+4 = 130^\circ`