Answer:
m∠C = 32°
m∠D = 82°
m∠DEC = 66°
Step-by-step explanation:
Exterior Angle Theorem says that the degree measure that with an angle forms a straight line (Ex. Angle DEF in the picture) is equal to the sum of the two other angles in the triangle. This means that the measure of angle DEF is equal to the measure of angle DCE plus the measure of angle CDE. This would mean that 9y + 1 + 3y + 5 = 114, meaning that 12y + 6 = 114, which means that 12y = 108, which means that y = 9. If we plug 9 in for all of these values, we get that angle D is 9 * 9 + 1, which is 82 and that angle C is 3 * 9 + 5, which is 32. Next, we know that the sum of angles in a triangle is 180, so we subtract 32 and 82 from 180 to find the measure of angle DEC, and this is 66 degrees.
