The measure of the angle m∠DCE is 56° if the value of x in the angles (9x - 31), (7x-2), and (4x + 33) is 18 option (C) is correct.
What is the triangle?
The triangle can be defined as a three-sided polygon in geometry and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.
We have measures of the exterior angles are:
(9x-31)°, (4x+33)°, and (7x-2)°
We know the sum of the exterior angles is 360°
(9x-31)°+(4x+33)°+(7x-2)° = 360°
20x = 360
x = 18° (divide by 20 on both sides)
Now the measure of the angle:
m∠DCE = 180° - (7x-2)°
Put x = 18 in the above equation, we get:
m∠DCE = 180° - (7(18)-2)°
m∠DCE = 180° - 124°
m∠DCE = 56°
Thus, the measure of the angle m∠DCE is 56° if the value of x in the angles (9x - 31), (7x-2), and (4x + 33) is 18 option (C) is correct.
Learn more about the triangle here:
brainly.com/question/25813512
