Explanation:
We can do a diagram of triangle CDE:
The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:
[tex]\begin{gathered} m\angle C+m\angle D+m\angle E=180º \\ (4x-16)+(6x-1)+(4x-13)=180 \\ (4x+6x+4x)+(-16-1-13)=180 \\ 14x-30=180 \end{gathered}[/tex]
Solve for x:
[tex]\begin{gathered} 14x=180+30 \\ 14x=210 \\ x=\frac{210}{14} \\ x=15 \end{gathered}[/tex]
And with x = 15, replace into the expression for the measure of angle C to find it:
[tex]m\angle C=4x-16=4\cdot15-16=60-16=44º[/tex]
Answer:
m
