Isosceles triangle,two angles have the same measure. Determine the measure of the third angle in an isosceles triangle,if the third angle is 10 more than one-half of either of the equal measurements
x = each base
vertex angle = 1/2x + 10
solve
x + x + 1/2x + 10 = 180
To determine the measure of the third angle in an isosceles triangle, we need to use the fact that two angles in the triangle have the same measure.
Let's denote the measure of the two equal angles as 'x'. According to the given information, we can say that the measure of the third angle is 10 more than one-half of either of the equal measurements.
Mathematically, we can represent this as:
Third angle = (1/2) * x + 10
Since the triangle is isosceles, the sum of the three interior angles is always 180 degrees. Therefore, we can write an equation:
x + x + [(1/2) * x + 10] = 180
Simplifying this equation will help us find the value of 'x' and, hence, the measure of the third angle.
2x + (1/2) * x + 10 = 180
(4/2)x + (1/2)x + 10 = 180
(5/2)x + 10 = 180
(5/2)x = 180 - 10
(5/2)x = 170
x = (2/5) * 170
x = 68
So, the measure of each of the two equal angles in the isosceles triangle is 68 degrees.
Now, to find the measure of the third angle, we substitute the value of 'x' into the equation we wrote earlier:
Third angle = (1/2) * x + 10
Third angle = (1/2) * 68 + 10
Third angle = 34 + 10
Third angle = 44
Therefore, the measure of the third angle in the isosceles triangle is 44 degrees.