In an isosceles triangle, the angle at the base is 30 degrees less than the angle opposite the base. Find what all the angles of the triangle are equal to.
In an isosceles triangle, the angles at the base are equal, we denote their degree measure as x;
Since the angle opposite to the base is 30 ° more than the angle at the base, then we denote it: x + 30;
Since the sum of any triangle is 180 °, we compose and solve the equation:
x + x + (x + 30) = 180;
x + x + x + 30 = 180;
3x + 30 = 180;
3x = 180 – 30;
x = 50 ° – angles at the base of the triangle;
(x + 30) = 50 + 30 = 80 ° – the angle of the apex of the triangle.
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