Question

Don't just straight up tell me the answer, tell me how to do it please!(30 points)

Answer 1

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°