Find the angle at the apex of an isosceles triangle if the angle at the base is known 72 °; 53 °; 45 °; 39 °; 49 °.

The sum of the angles in any triangle is 180 °. In an isosceles triangle, the angles at the base are equal, therefore:

If the angles at the base are 72 °, then the angle at the apex is: 180 ° – 72 ° – 72 ° = 36 °;
If the angles at the base are 53 °, then the angle at the apex is: 180 ° – 53 ° – 53 ° = 74 °;
If the angles at the base are 45 °, then the angle at the top is: 180 ° – 45 ° – 45 ° = 90 °;
If the angles at the base are 39 °, then the angle at the apex is: 180 ° – 39 ° – 39 ° = 102 °;
If the angles at the base are 49 °, then the angle at the apex is: 180 ° – 49 ° – 49 ° = 82 °.