When we have a quadrilateral inscribed in a circle, we can use the Inscreibed Quadrilateral Theorem to infere about opposite angles of this quadrilateral.
The theorem says that the sum of opposite angles of a quadrilateral inscribed in a circle will always be 180°.
In this case, we have that:
[tex]\angle C+\angle D=180\degree[/tex]
Because they are opposite angles of a quadrilateral inscribed in a circle.
Thus, let's substitute its expressions and solve for x:
[tex]\begin{gathered} 7x+20+9x-4=180 \\ 16x+16=180 \\ 16x=164 \\ x=\frac{164}{16}=\frac{41}{4} \end{gathered}[/tex]
Now, to calculate the angle ECB, we can substitute x into the expression for the angle ECB:
[tex]\angle ECB=7x+20=7\cdot\frac{41}{4}+20=71.75+20=91.75[/tex]
Thus, the angle ECB is 91.75°, alternative 2.
