Question

Given △ABC≅△JKL, m∠B=55°, and m∠L=25°, what is the measure of ∠J?

Answer 1

100°

Explanation:

Using the congruence statement, we know that ∠A≅∠J, ∠B≅∠K, and ∠C≅∠L.∠

Since m∠B = 55, then m∠K = 55.

Along with ∠L, this gives us 2 of the 3 angles of triangle ABC. We know that the sum of the measures of the angles in a triangle is 180°; this means that

∠J = 180-(55+25) = 180-80 = 100°

Answer 2

For the answer to the question above,
<J = 100
because they are similar they have the same angles
The two triangles are similar, so they must have corresponding angles. Thats one way to define similarity, it can dilate (zoom in /zoom out) , but the angles are preserved. You can also define similarity in terms of the proportionality of the sides.

"Given △ABC≅△JKL"

The order of the letters counts.
<A = <J
<B = <K
<C = <L

now you can draw two generic triangles, which have the same three angles, but label the angles accordingly, so they match up.

then by correspondance we can fill in
nightowlthe third angle can be found by the fact that
the three angles must add up to 180.