In a triangle MNP MN = MP, the angle NMP is 72 degrees. Find the value of the angle adjacent to the angle MNP.

If the side of the triangle MN is equal to the side of MP, then the triangle MNP is isosceles. The property of an isosceles triangle states that not only the sides are equal in it, but also the angles at its base. Hence the MPN angle is equal to the MNP angle. The sum of the angles of any triangle is 180 °, therefore PNM + MNP = 180 ° – PMN = 180 ° – 72 ° = 108 °; PNM = MNP = 108/2 = 54 °.

The sum of the adjacent angles is 180 °, since they make up the unfolded angle. Therefore, the angle adjacent to the angle MNP will be equal to the difference: 180 ° – MNP = 180 ° – 54 ° = 126 °.