The measure of ∠DCB is 128°.
The measure of ∠ECD is 52°
Step-by-step explanation:
- At the point of intersection, the opposite angles are equal.
- Therefore, ∠ACB = ∠ECD and ∠ACE = ∠DCB
- The measure of angle in straight line is 180°.
∠ACB + ∠ACE = 180°
(x+11)° + (3x+5)° = 180
⇒ 4x+16 = 180
⇒ 4x = 164
⇒ x = 164/4
x = 41°
∠DCB = ∠ACE ⇒ (3x+5)°
∠DCB = 3(41)+5 = 128°
∠ECD =∠ACB ⇒ (x+11)°
∠ECD = 41+11 = 52°
