Determine the angles of an isosceles triangle ARM if the outer angle of the apex angle R is 129 °.

We are given an isosceles triangle ARM, and we also know that the outer angle at the vertex R is 129 °.

In order to find the remaining angles, we apply the properties of the angles of an isosceles triangle and the theorem on the sum of the angles of a triangle.

First option.

Find the inner corner of the triangle adjacent to the outer corner. The sum of adjacent angles is 180 °.

180 ° – 129 ° = 51 °.

If this is an angle at the base, then two angles are 51 ° each and an angle at the apex of 180 ° is 2 * 51 ° = 78 °.

Second option.

51 ° – apex angle.

(180 ° – 51 °) / 2 = 129 ° / 2 = 64.5 ° angles at the base.