Angle Properties of Circles

O is the centre and PT is a tangent to the circle at T. AOT and BOP are straight lines. Find the values of a and b.

• a = 85⁰, b = 80⁰

• a = 80⁰, b = 80⁰

• a = 85⁰, b = 85⁰

• a = 80⁰, b = 85⁰

O is the centre, PA is a tangent to the circle at A. AOC and PBC are straight lines. Find the values of x, y and z.

• x = 60⁰, y = 30⁰

  and z = 90⁰

• x = 30⁰, y = 60⁰

  and z = 90⁰

• x = 60⁰, y = 60⁰

  and z = 90⁰

• x = 90⁰, y = 30⁰

  and z = 60⁰

O is the centre, PA is a tangent to the circle at A. EOC and DOA are straight lines. Find the values of x, y and z.

• x = 100⁰, y = 40⁰

  and z = 50⁰

• x = 140⁰, y = 20⁰

  and z = 70⁰

• x = 120⁰, y = 30⁰

  and z = 60⁰

• x = 150⁰, y = 15⁰

  and z = 75⁰

O is the centre, PA and QA are tangents to the circle at P and Q respectively. Find the values of a, b and c.

• a = 75⁰, b = 75⁰

  and c = 60⁰

• a = 80⁰, b = 80⁰

  and c = 50⁰

• a = 45⁰, b = 45⁰

  and c = 30⁰

• a = 90⁰, b = 90⁰

  and c = 30⁰

O is the centre, PA and QA are tangents to the circle at P and Q respectively. Find the values of a, b and c.

• a = 11.5⁰, b = 75⁰

  and c = 37.5⁰

• a = 23⁰, b = 90⁰

  and c = 67⁰

• a = 23⁰, b = 90⁰

  and c = 23⁰

• a = 11.5⁰, b = 60⁰

  and c = 30⁰

O is the centre of the circle. PA and PB are tangents to the circle at A and B respectively. Find the value of x.

O is the centre of the circle.

PA and PB are tangents to the circle at A and B respectively.

Find the value of x.

O is the centre of the circle. PA and PB are tangents to the circle at A and B respectively. AODC and PBC are straight lines. Find the value of a, b and c.

• a = 55⁰, b = 70⁰ 

  and c = 90⁰

• a = 55⁰, b = 70⁰ 

  and c = 55⁰

• a = 65⁰, b = 35⁰ 

  and c = 90⁰

• a = 35⁰, b = 35⁰ 

  and c = 55⁰

Given that BD = DC, ∠ABD = 42⁰ and ∠DBC = 65⁰,

calculate

∠DEC

Answer explanation

Angles in ΔDEC

∠D = 50⁰ [previously answered]

∠C = 42⁰ (angles from same segment as ∠ABD)

Hence, ∠E = 180 - 50 - 42

Find the values of x and y.

• x = 30⁰, y = 30⁰

• x = 80⁰, y = 30⁰

• x = 30⁰, y = 80⁰

• x = 15⁰, y = 40⁰