The angle subtended by a diameter of a circle at the circumference is a/an

Analyze the question: We are asked about the angle formed at any point on the circumference of a circle by the two ends of a diameter. This is a classic circle theorem.

The concept (Angle in a Semicircle): A diameter divides a circle into two semicircles. The angle at the centre on the diameter's side is a straight angle (180°). The angle at the circumference is half the angle at the centre, so:

Angle at circumference = ½ × 180° = 90°

Step-by-step solution:

1. Let AB be a diameter of the circle, and let C be any point on the circumference (not A or B).
2. The angle at the centre subtended by AB is 180°, since AB is a straight line through the centre.
3. By the circle theorem (the angle at the centre is twice the angle at the circumference, both standing on the same arc): ∠ACB = 180° ÷ 2 = 90°
4. An angle of 90° is a right angle.

Checking the options:

• A. Acute (less than 90°): no
• B. Obtuse (between 90° and 180°): no
• C. Reflex (more than 180°): no
• D. Right angle (exactly 90°): yes
• E. Supplementary: this describes a pair of angles adding to 180°, not a single angle of 90°, so no

Exam tip: Remember "angle in a semicircle = 90°." Whenever you see a diameter in a circle problem, look for a triangle with its third vertex on the circle. That triangle is right-angled, and you can use Pythagoras or angle sums to continue. This shortcut appears often in JAMB, WASSCE and NECO.