Answer:
x=17
Step-by-step explanation:
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
In the triangle ABC
m∠A+m∠B+m∠C=180°
substitute the values and solve for m∠C
4x+49°+m∠C=180°
m∠C=180°-49°-4x
m∠C=131°-4x
In the triangle EDC
m∠E+m∠D+m∠C=180°
we have
m∠E=x
m∠D=100°
m∠C=131°-4x -----> by vertical angles
substitute the values
[tex]x+100\°+(131\°-4x)=180\°\\-3x+231\°=180\°\\3x=231\°-180\°\\3x=51\°\\x=17[/tex]
