In an equilateral triangle ABC, the medians BK and AM meet at point O. Find ∠AOK.

In order to find the value of the angle AOK in an equilateral triangle ABC, given that the medians BK and AM intersect at point O, you first need to remember the rules.
1.) In an equilateral triangle, all angles are equal and the magnitude of each angle is 60 °.
2.) In an equilateral triangle, medians are also bisectors and heights.
Now consider ΔAOK.
1.) Since BK is perpendicular to the base of AC, then OK is perpendicular to AC.
So it can be written for the OKA angle.
OKA = 90 °.
2.) Now let’s find the value of the angle OAK.
To do this, we will write for the angle BAC.
BAC = BAO + OAK.
Since AM or AO are bisectors, we will write.
BAO = OAK.
BAC = 2OAK.
60 ° = 2OAK.
OAK = 60 °: 2.
OAK = 30 °.
3.) Now we write for the angles ΔAOK.
OKA + OAK + AOK = 180 °.
90 ° + 30 ° + AOK = 180 °.
120 ° + AOK = 180 °.
AOK = 180 ° – 120 °.
AOK = 60 °.
Answer: 60 °.