Two beams BD and BK are drawn from the top of the unfolded angle ABC, so that the angle ABK = 128 degrees

Two beams BD and BK are drawn from the top of the unfolded angle ABC, so that the angle ABK = 128 degrees, the angle CBD = 164 degrees. Calculate the angle DBK.

The angles AВK and KВС are adjacent (and the sum of adjacent ones is 180˚), so we find the angle КВС:

∟KВС = 180˚ – 128˚ = 52˚.

Beam BD divides the DBC angle into two angles – DBC and PBC, which is 164 16 in total. Find the angle DВК:

∟ DBK = ∟DBC – ∟KВС = 164˚ – 52˚ = 112˚.

Answer. ∟ DBK = 112˚.