If ∠ABC = (2x + 25)°, then the value of ∠ACB:

The correct answer is Option (3) → 100°

An exterior angle of a triangle equals the sum of the two interior opposite angles. Here the exterior angle at C is \(\angle ACD\), and the interior opposite angles are \(\angle A\) and \(\angle B\).

Finding \(x\) (exterior angle at C):

• Exterior angle = sum of the interior opposite angles: \((2x+30)=(x-20)+(2x+25)\)

• \(2x+30=3x+5\)

• \(x=25\)

The angles:

• \(\angle ACD=2\times25+30=80^\circ\)

• \(\angle ACB=180^\circ-80^\circ=100^\circ\) (angles on the straight line BD)

Tip: The question asks for \(\angle ACB\), the interior angle. \(80^\circ\), Option (4), is the exterior angle \(\angle ACD\), and \(75^\circ\), Option (2), is \(\angle ABC\).