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It is required to construct an isosceles triangle such that the vertex angle shall be 5 degree greater than half a base angle. How large should the angles

We let X be the measure of the base angle. We write: (5 + (1/2)X) + X + X = 180 --> (1/2)X + X + X = 175 --> [(5/2)X = 175]2 --> 5X = 350 --> X = 70. So the angles must be: 70°, 70°, 40°.