There are two similar triangles. The angles are: from top to bottom left: DE, from bottom left to right: EF, And from Top to bottom right corner: DF. DE: 10.32 cm.EF: 8.88 cm.FD 12.24 cm. The angles are: D,top,45 Degrees. E, bottom left corner, 79 Degrees. And F, Bottom right corner, 56 Degrees. On the other Triangle, The sides are SQ, Top to bottom left corner. QR, Bottom left to right.And SR, Top to bottom right. SQ:4.3 cm,QR: 3.7 cm and SR: 5.1 cm. What is Angle R?

Since the sides are in common ratio between triangles, the triangles are similar. So, corresponding angles are equal.

Angle R id congruent to Angle F.

To find Angle R, we can use the property of similar triangles. The two triangles are similar because they have the same shape but different sizes. In similar triangles, corresponding angles are equal, and corresponding sides are proportional.

In the first triangle (DEF), we are given three side lengths: DE (10.32 cm), EF (8.88 cm), and FD (12.24 cm). We are also given three angles: Angle D (45 degrees), Angle E (79 degrees), and Angle F (56 degrees).

In the second triangle (SQR), we are given three side lengths: SQ (4.3 cm), QR (3.7 cm), and SR (5.1 cm). We want to find Angle R.

First, let's compare the corresponding sides of the two triangles:

DE/SQ = EF/QR = FD/SR

Using the given values:

10.32/4.3 = 8.88/3.7 = 12.24/5.1

Simplifying these ratios, we get:

2.4 = 2.4 = 2.4

This tells us that the sides of the two triangles are proportional.

Next, let's compare the corresponding angles of the two triangles:

Angle D = Angle S
Angle F = Angle R

Therefore, Angle R is equal to Angle F, which is given as 56 degrees.

So, Angle R is 56 degrees.