Respuesta :

IcedTea
AA Similarity Postulate means Angle Angle Congruency which means that <A and <D are both 55° and <B and <E are both 60°

So, to solve for C, since a triangle has a total of 180° you subtract 180-55-60 to get C.

m<C = 65°

Hope this helped :)
calculista

Answer:

[tex]m<C=65\°[/tex]

Step-by-step explanation:

we know that

If two triangles are similar, then its corresponding angles are congruent

so

m<A=m<D

m<C=m<F

m<B=m<E

step 1

Find the measure angle B

we have

[tex]m<E=60\°[/tex]

so

[tex]m<B=60\°[/tex] ------> by corresponding angles

step 2

Find the measure angle C

we know that

[tex]m<A+m<B+m<C=180\°[/tex] ----> the sum of the interior angles in a triangle must be equal to [tex]180\°[/tex]

we have

[tex]m<A=55\°[/tex]

[tex]m<B=60\°[/tex]

substitute

[tex]55\°+60\°+m<C=180\°[/tex]

[tex]m<C=180\°-55\°-60\°=65\°[/tex]