Given △ABC∼△DEF , m∠A=52° , and m∠E=11° , what is the measure of angle C ?(1 point)
The measure of angle C can be found using the concept of corresponding angles in similar triangles.
m∠C = m∠A + m∠B (since the sum of angles in a triangle is 180°)
m∠B = 180° - m∠A - m∠C
m∠B = 180° - 52° - m∠C
m∠B = 128° - m∠C
Using the fact that △ABC∼△DEF, we can set up a proportion:
AB/DE = BC/EF = AC/DF
Since we need to find the measure of angle C, AC corresponds to DF.
AC/DF = BC/EF
AC/DF = AC/(DE*sin(52°))
This simplifies to:
1 = 1/(DE*sin(52°))
DE = 1/sin(52°)
Now, we can find the measure of angle C using the corresponding angles concept:
AC/DF = AC/(DE*sin(52°)) = AC/(1/sin(52°)*sin(52°)) = AC/1 = AC
Therefore, the measure of angle C in △ABC is 52°.