the other two angles must be equal, call each one x
2x + 58 = 180
solve for x
2x + 58 = 180
solve for x
Given that one angle measures 58°, we have:
Angle A = 58°
Since the triangle is isosceles, we have:
Angle B = x
Angle C = x
The sum of the angles in a triangle is always 180°, so we can write the equation:
Angle A + Angle B + Angle C = 180°
Substituting the known values:
58° + x + x = 180°
Simplifying the equation:
58° + 2x = 180°
Subtracting 58° from both sides:
2x = 180° - 58°
2x = 122°
Dividing both sides by 2:
x = 61°
So, the possible measures for the other two angles are 61° each.
In this case, we are given that one of the angles measures 58°. Therefore, we can set up the equation:
x + x + 58° = 180°
Simplifying the equation:
2x + 58° = 180°
Subtracting 58° from both sides:
2x = 180° - 58°
2x = 122°
Dividing both sides by 2:
x = 61°
Now we know that the base angles (congruent angles) are 61° each.
To find the measure of the third angle, we can subtract the sum of the two base angles from 180°:
Third angle = 180° - (61° + 61°)
Third angle = 180° - 122°
Third angle = 58°
Therefore, the other two possible angles in the isosceles triangle are 61° and 58°.