Question

A, B, C and D are points on a circle, centre o

AOC is a diameter of the circle.
a
Angle BAC = 55°
Work out the size of angle ADB
Give a reason for each stage of your working.

Answer 1

∠ADB = 35°

Explanation:

The angle at the circumference in a semicircle is a right angle.

⇒ ∠ABC = 90°

Interior angles in a triangle sum to 180°

⇒ ∠BAC + ∠ABC + ∠BCA = 180°

⇒ 55° + 90° + ∠BCA = 180°

⇒ ∠BCA = 35°

The angles at the circumference subtended by the same arc are equal (angles in the same segment are equal)

⇒ ∠ADB = ∠BCA

⇒ ∠ADB = 35°