To find the measure of angle C using the Triangle Angle Sum Theorem, we need to know the measures of the other two angles in the triangle. The theorem states that the sum of the angles in a triangle is 180°.
If we let angle A and angle B represent the two known angles in the triangle, we can use the formula:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180° \]
Let's denote angle C as x:
\[ \text{Angle A} + \text{Angle B} + x = 180° \]
Rearranging gives us:
\[ x = 180° - (\text{Angle A} + \text{Angle B}) \]
Without the measures of angle A and angle B, we cannot determine the exact measure of angle C. However, if you can provide the measures of angle A and angle B, we can calculate angle C.
If we assume the angles are:
- If angle A = 155° and angle B = 155°, it would be impossible since the sum exceeds 180°.
- If angle A = 155° and angle B = 65°, then: \[ x = 180° - (155° + 65°) = 180° - 220° = -40° , (\text{not valid}) \]
- If angle A = 65° and angle B = 65°, then: \[ x = 180° - (65° + 65°) = 180° - 130° = 50° , (\text{not an option}) \]
- If angle A = 55° and angle B = 65°: \[ x = 180° - (55° + 65°) = 180° - 120° = 60° , (\text{not an option}) \]
- If angle A = 65° and angle B = 55°: \[ x = 180° - (65° + 55°) = 180° - 120° = 60° , (\text{not an option}) \]
Thus, with the assumed values for A and B, no angles fulfill valid triangle criteria unless provided specifically. Please confirm or provide the values for angle A and angle B to proceed!
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