14) Given a right-angled triangle with angles 70° and α, and one leg of length indicated by a tick mark. Another leg is longer and indicated by two tick marks. Find the angle α.

Solution:

In a right-angled triangle, the sum of the two acute angles is 90°.

\( \alpha + 70^{\circ} = 90^{\circ} \)

\( \alpha = 90^{\circ} - 70^{\circ} \)

\( \alpha = 20^{\circ} \)

The tick marks indicate that the sides are equal, which would imply a 45-45-90 triangle if they were the legs. However, given the 70° angle, the tick marks likely indicate something else or are misleading for this specific calculation of α. We rely on the sum of angles in a right triangle.

Answer: \(\alpha = 20^{\circ}\)