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The problem is as follows:

1. **Given**:
   - Triangle \( ABX \) is a right triangle.
   - The ratio of the perimeters of triangles \( ABX \) and \( ADX \) is \( 5:2 \).
   - \( m \angle AXB = 90^\circ \).
   - \( m \angle ABX = 2x \).

2. **Find**:
   - The measure of \( m \angle BAX \) (denoted as \( y \)).
   - The measure of \( m \angle ABX \) (denoted as \( 2x \)).

To solve this, let's denote:
- \( AB = a \), \( AX = b \), \( BX = c \), and \( AD = d \).

We will use the given ratio and angle information to find the unknown measures. Let's solve step-by-step:

1. **Perimeters Relation**: Use the ratio \( 5:2 \) to express the relationship between the perimeters.
2. **Right Triangle Relationships**: Use trigonometric identities or Pythagoras' theorem to solve for \( x \) and \( y \).

Let me know if you want me to continue this way!

Given a right triangle. The ratio of the perimeters of triangle ABX and triangle ADX is 5:2. Find m∠AXB (Hint: m∠AXB = 90° and m∠ABX = 2x).

Learn how to calculate the angles in a right triangle with a given ratio of perimeters. This problem demonstrates key geometric concepts like perimeter ratios, right triangle properties, and trigonometric methods. Suitable for students in Grades 9-11.

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