The image shows a right triangle with the following information:

• Side $AD = 4$
• Side $AB = 5$
• Side $BC = 4$

You're asked to find the measure of angle $\angle ABC$ in degrees.

Since the triangle is a right triangle (the right angle is marked at $D$), you can use trigonometry to find $\angle ABC$. The tangent function is useful here, as it relates the opposite side to the adjacent side in a right triangle.

The formula for tangent is: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

In this case, the opposite side to $\angle ABC$ is $AD = 4$, and the adjacent side is $BC = 4$.

So: $\tan(\angle ABC) = \frac{4}{4} = 1$

Now, find the angle whose tangent is 1. This corresponds to: $\angle ABC = \tan^{-1}(1) = 45^\circ$

Thus, the measure of $\angle ABC$ is $45^\circ$.

Would you like further details or have any questions? Here are some related questions:

1. How do you use other trigonometric functions to find angles in right triangles?
2. Can the Pythagorean theorem be used to check the sides of a right triangle?
3. How do you find the other angle in a right triangle when one is known?
4. What is the difference between sine, cosine, and tangent functions in trigonometry?
5. How do you calculate angles using the sine or cosine rule?

Tip: Remember to use a calculator in degree mode when working with trigonometric functions!