Triangle MPK is isosceles with base MP. Line AB is parallel to side KP; A belongs to MK, B belongs to MP

Triangle MPK is isosceles with base MP. Line AB is parallel to side KP; A belongs to MK, B belongs to MP. Find angle MAB and angle ABM if angle K = 72 degrees, angle M = 54 degrees.

The MPK triangle is isosceles, with the base MP, and the angle M = 54 degrees, which means that the angles at the base of M and P will be 54 °, by the property of an isosceles triangle. Line AB is parallel to side KP; A belongs to MK, B belongs to MP, which means that the angle MAB will be corresponding to the angle K, and the angle ABM will be corresponding to the angle P. We get that the angle ABM and angle P will be equal to 54 °, as the corresponding angles with AB parallel to KP and secant MP. By condition, the angle is K = 72 degrees. Then the angle MAB and angle K will be equal to 72 °, as the corresponding angles at AB parallel KP and secant MK. Answer: The MAB angle is 72 ° and the ABM angle is 54 °.