According to the Triangle Angle Sum Theorem, the sum of the angles in a triangle is 180°. If the first angle is 25°, we can use the theorem to find the measure of angle C.
Let's denote the angles of the triangle as:
- Angle A = 25°
- Angle B (unknown)
- Angle C (unknown)
Using the theorem: \[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
Since we need to find angle C and we do not have the measure of angle B, we can express it in terms of angle C:
Rearranging gives: \[ \text{Angle B} + \text{Angle C} = 180° - 25° \] \[ \text{Angle B} + \text{Angle C} = 155° \]
Without additional information about angle B, we cannot find a specific value for angle C yet. If you want to find an angle based solely on a known value, we can explore if angle B is known or if there’s a way to solve for angle C directly.
However, if one of the choices given (155°, 205°, 65°, 55°) is meant for angle C without knowledge of B, we would normally consider that angle C could likely take the complement of angle B. Let's evaluate those choices:
- 155°: This means angle B would be 0°, which is not a valid triangle.
- 205°: This exceeds the maximum angle for any triangle (180°), so it's invalid.
- 65°: This implies that angle B would be 90° (155° - 65°), which is valid.
- 55°: This implies angle B would then be 100°, which is also valid.
From the provided options, 65° is the only choice that maintains the property of a triangle where Angle B can be respected as an angle of a triangle as well.
Thus, if we guess at a reasonable combination from the values, angle C would likely be 65°, making angle B valid.
So the answer is: 65°.
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