The problem states that Daniel drew a right-angled triangle with two equal-length sides. This type of triangle is called an isosceles right triangle.

Solution:

In a right triangle, the sum of all angles is 180°, and one angle is always 90° (the right angle). Since the other two sides are equal, the angles opposite these sides must also be equal.

Let the angles be:

1. $90^\circ$ (right angle)
2. $x^\circ$
3. $x^\circ$

The total sum of angles in the triangle is: $90^\circ + x + x = 180^\circ$

Simplifying: $90^\circ + 2x = 180^\circ$

Subtract $90^\circ$: $2x = 90^\circ$

Divide by 2: $x = 45^\circ$

Final Answer:

The three angles in the triangle are:

1. $90^\circ$ (the right angle)
2. $45^\circ$
3. $45^\circ$

Would you like me to expand on this or provide a visual explanation?

Related Questions:

1. What is an isosceles right triangle, and how is it different from other triangles?
2. How do you calculate the angles of any triangle given specific side lengths?
3. Can you prove why the sum of the angles in any triangle is always $180^\circ$?
4. What is the relationship between the sides and angles in a right triangle?
5. How can trigonometric functions (like sine and cosine) be used to verify these angles?

Tip:

In an isosceles right triangle, the two legs are equal, and the hypotenuse is always $\sqrt{2}$ times the length of one leg!