17) Given a triangle with tick marks on two sides, indicating they are equal, and a right angle. Find the angle α.

Solution:

The triangle is a right-angled isosceles triangle because two sides are marked as equal and there is a right angle. In an isosceles right-angled triangle, the two acute angles are equal.

The sum of angles in a triangle is 180°.

Let the two equal acute angles be \( \alpha \).

\( \alpha + \alpha + 90^{\circ} = 180^{\circ} \)

\( 2\alpha = 180^{\circ} - 90^{\circ} \)

\( 2\alpha = 90^{\circ} \)

\( \alpha = \frac{90^{\circ}}{2} \)

\( \alpha = 45^{\circ} \)

Answer: \(\alpha = 45^{\circ}\)