Answer:
DCE is 54°
Step-by-step explanation:
To solve this, we must come up with an equation. Since D, C, and E are each straight lines, they are each 180°. then, each line is separating the other which splits the 180 degree line into two parts. For example, E separates D, C separates E, and so on. The exterior angles are given, but the interior aren't. So:
for angle EDC: 180 - (9x - 31)
for angle CED: 180 - (4x + 33)
for angle DCE: 180 - (7x - 2)
we know that all angles in a triangle add up to 180°. So, our equation is:
180 - (9x - 31) + 180 - (4x + 33) + 180 - (7x - 2)=180.
simplify:
180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2=180
540 - 20x = 180
540 - 180 = 20x
360=20x
x= 18
for angle EDC: 180 - (9•18 - 31)=49°
for angle CED: 180 - (4•18 + 33)=75°
for angle DCE: 180 - (7•18 - 2)=54°
