Question

In ACDE, mC = (5x + 18), mZD (5x + 18)°, m_D = (3x + 2)°, and mZE (x + 16). Find m2D.

Answer 1

In this proble we have an expression for each angle of the triangle so we can us the property that the sum of the internal angles of a triangle must be equal to 180 so the expression will be:

`5x+18+3x+2+x+16=180`

So we can solve the expression for x so:

`\begin{gathered} 9x+36=180 \\ 9x=180-36 \\ x=(144)/(9) \\ x=16 \end{gathered}`

Now with the value of x we can calculate the angle D that will be equal to:

`\begin{gathered} \angle D=3(16)+2 \\ \angle D=48+2 \\ \angle D=50 \end{gathered}`