Angles ABC and DBC are adjacent, ray BM belongs to angle ABC, ray BK belongs to angle DBC, angle MBC

Angles ABC and DBC are adjacent, ray BM belongs to angle ABC, ray BK belongs to angle DBC, angle MBC = angle CBK = 30 degrees, angle DBK is 5 times the angle ABM Find angles ABC and DBC.

Since the sum of adjacent angles is 180, then ABM + MBC + СBK + KMD = 180.

By condition, MBC = СBК = 30, and KBD = 5 * ABM. Let the angle ABM = X0, then the angle KBD = 5 * X.

Substitute all the angles.

180 = X + 30 + 30 + 5 * X.

180 = 6 * X + 60.

6 * X = 180 – 60 = 120.

X = 120/6 = 20.

Angle ABM = 20, then KBD = 5 * 20 = 100.

Let’s find the angle ABC.

ABC = ABM + MBC = 20 + 30 = 50.

Let’s find the corner of the internal combustion engine.

ABC = CBK + KBD = 30 + 100 = 130.

Answer: ABC = 50, ABC = 130.