Given △ABC∼△DEF, m∠A=52°, and m∠E=11°, what is the measure of angle C?(1 point)
m∠C =
To find the measure of angle C, we can use the fact that corresponding angles of similar triangles are equal.
Since △ABC∼△DEF, we know that the ratios of corresponding sides are equal. Let's label the ratio as k:
AB/DE = BC/EF = AC/DF = k
From the given information, we know that m∠A = 52° and m∠E = 11°.
In △ABC, the sum of the angles is 180°. So we can find the measure of angle C by subtracting the sum of angles A and B from 180°:
m∠C = 180° - m∠A - m∠B
But we don't know the measure of angle B.
Let's use the ratio of corresponding sides to find the measure of angle B in △DEF using the fact that corresponding angles of similar triangles are equal:
BC/EF = AC/DF
Now, let's substitute the values we know:
BC/EF = AC/DF
BC/EF = AB/DE (since AB/DE = AC/DF = k)
BC/EF = 1 (let's assume AB/DE = 1)
BC = EF
So in △DEF, BC is equal to EF. Since BC and EF are corresponding sides, angle B and angle F are corresponding angles and are equal.
Therefore, we can conclude that m∠B = m∠F.
Now we have enough information to find the measure of angle C using the equation:
m∠C = 180° - m∠A - m∠B
m∠C = 180° - 52° - 11°
m∠C = 117°
Therefore, the measure of angle C is 117°.
To find the measure of angle C, we can use the fact that corresponding angles of similar triangles are congruent.
Given that △ABC∼△DEF, it means that the corresponding angles of these triangles are equal. Hence, angle A corresponds to angle D, angle B corresponds to angle E, and angle C corresponds to angle F.
We are given that the measure of angle A is 52°, and the measure of angle E is 11°. Since angle A corresponds to angle D, we can conclude that angle D is also 52°.
Similarly, angle B corresponds to angle E, so angle B is also 11°.
Now, to find the measure of angle C, we need to find the corresponding angle in △DEF. We know that angle F corresponds to angle C.
Since angle D is 52° and angle B is 11°, the sum of the measures of angles D and B is 52° + 11° = 63° (as the sum of angles in a triangle is always 180°).
Therefore, the measure of angle F (corresponding to angle C) can be found by subtracting 63° from 180°:
m∠F = 180° - 63° = 117°.
So, the measure of angle C is 117°.
117°
Well, if triangle ABC is similar to triangle DEF, then that means their corresponding angles are congruent. So if angle A measures 52°, then angle E must also measure 52°.
But you asked for the measure of angle C, not E. So let's play a little game of math tag.
Since angle A and angle E are congruent, that means angle C and angle F must also be congruent. So, if angle E measures 52°, angle F must also measure 52°.
So, the measure of angle C is 52°! Ta-da!