Thales’ Theorem

Thales’s theorem states that if a triangle is formed using the diameter of a circle and any point on the semicircle, it will always be a right-angled triangle.

In the diagram, AB is the diameter of the circle, and C is a point on the semicircle. No matter where C is, the angle at C is always 90°.

• Step 1: Use Thales’s Theorem
  Since $AB$ is the diameter, and vertex $C$ is a point on the semicircle. Thus,

$$ \angle C = 90^\circ $$

• Step 2: Find the Remaining Angle
  The sum of all angles in a triangle is:

$$ \angle A + \angle B + \angle C = 180^\circ $$

Since we know $ \angle C = 90^\circ $ and $ \angle A = 35^\circ $, we can find $ \angle B $:

$$ \angle B = 180^\circ – 90^\circ – 35^\circ = 55^\circ $$