The image shows a math problem involving two congruent triangles, $\triangle ABC \cong \triangle DEF$. The task is to find the measure of given angles, with the following information provided:

• $m \angle A = x + 21$
• $m \angle D = 2x$

Since the triangles are congruent, corresponding angles are equal. Therefore, $m \angle A = m \angle D$.

We can set up the equation: $x + 21 = 2x$ Now, solving for $x$:

$x + 21 = 2x$ $21 = 2x - x$ $21 = x$

So, $x = 21$.

To find $m \angle A$, substitute $x = 21$ into the expression for $m \angle A$:

$m \angle A = 21 + 21 = 42^\circ$

Thus, $m \angle A = 42^\circ$.

Would you like more details, or do you have any questions?

Here are five related questions:

1. How do you solve equations involving variables on both sides?
2. What are the properties of congruent triangles?
3. How do corresponding parts of congruent triangles relate to each other?
4. How can angle measures be used to determine triangle congruence?
5. What are other ways to prove triangle congruence (e.g., SSS, SAS)?

Tip: When dealing with congruent triangles, always check that corresponding sides and angles are equal!