In an isosceles triangle, at least two sides are of equal length, and the angles opposite those sides are equal. Given that angle B measures 130 degrees, we can deduce important information about angles A and C.
Since the sum of all angles in any triangle is always 180 degrees, we can first calculate the sum of the angles A and C:
Angle A + Angle C + Angle B = 180 degrees
Substituting the value of angle B:
Angle A + Angle C + 130 degrees = 180 degrees
This simplifies to:
Angle A + Angle C = 50 degrees
Now, because triangle ABC is isosceles, angles A and C must be equal (as they are the angles opposite the equal sides). Therefore, we can set:
Angle A = Angle C
Let’s denote the measure of each angle as x:
x + x = 50 degrees
Which simplifies to:
2x = 50 degrees
Dividing by 2 gives us:
x = 25 degrees
Thus, both angle A and angle C must measure 25 degrees each.
In summary, the statement that must be true in this scenario is:
In triangle ABC, Angle A = 25 degrees and Angle C = 25 degrees.
This conclusion follows from the properties of isosceles triangles and the triangle angle sum theorem.