Given △ABC∼△DEF, m∠A=52°, and m∠E=11°, what is the measure of angle C?(1 point)
By triangle similarity, we have that the ratios of corresponding sides of similar triangles are equal. Therefore, we can set up the following ratios:
AB/DE = BC/EF = AC/DF.
We are given that m∠A = 52°, and m∠E = 11°. By corresponding angles of similar triangles, this means that m∠B = 11°.
Since the sum of angles in a triangle is always 180°, we can find the measure of angle C by subtracting the measures of angles A and B from 180°:
m∠C = 180° - (m∠A + m∠B) = 180° - (52° + 11°) = 180° - 63° = 117°.
Therefore, the measure of angle C is 117°.
To find the measure of angle C, we can use the property of corresponding angles in similar triangles.
Since △ABC ∼ △DEF, corresponding angles have the same measures.
We know that m∠A = 52° and m∠E = 11°.
Therefore, m∠C corresponds to m∠F.
So, the measure of angle C is equal to the measure of angle F, which is 11°.
To find the measure of angle C in triangle ABC, we can use the fact that corresponding angles in similar triangles are congruent.
Given that triangle ABC is similar to triangle DEF, we know that angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.
Since we are given that angle A measures 52° and angle E measures 11°, we can conclude that angle D also measures 52° (corresponding angles are congruent).
To find the measure of angle C, we need to determine the measure of angle F. Since angles in a triangle add up to 180°, we can set up an equation:
angle C + angle D + angle F = 180°
Substituting the values we know:
angle C + 52° + 11° = 180°
Simplifying the equation:
angle C + 63° = 180°
To isolate angle C, we subtract 63° from both sides:
angle C = 180° - 63°
Solving:
angle C = 117°
Therefore, the measure of angle C is 117°.