Given △ABC∼△DEF , m∠A=52° , and m∠E=11° , what is the measure of angle C ?(1 point)
m∠C =
Since △ABC∼△DEF, the corresponding angles are congruent. So, m∠C = m∠F. Since m∠E + m∠F + m∠C = 180°, we can solve for m∠C.
m∠C = 180° - m∠E - m∠F
m∠C = 180° - 11° - m∠F
Since m∠A + m∠B + m∠C = 180°, and m∠A = 52°, we can solve for m∠C.
m∠C = 180° - m∠A - m∠B
m∠C = 180° - 52° - m∠B
Equating the two expressions for m∠C, we have:
180° - 11° - m∠F = 180° - 52° - m∠B
Subtracting 180° from both sides, we have:
-11° - m∠F = -52° - m∠B
Rearranging the equation, we have:
m∠B - m∠F = -52° + 11°
Simplifying, we have:
m∠B - m∠F = -41°
Since m∠B = ∠C, we can rewrite the equation as:
m∠C - m∠F = -41°
Adding m∠F to both sides, we have:
m∠C = -41° + m∠F
Since m∠F = 11°, we can substitute that value into the equation:
m∠C = -41° + 11°
Simplifying the equation, we have:
m∠C = -30°
However, angle measures cannot be negative. Therefore, there is no valid measure for angle C given the given information.