Angles in Circles - Sample Questions

Please enter the answers in the boxes by each question, then click on the button at the end of the page to mark your answers.

Remember, angles are specified by three letters, marked in order, so in the diagram on the right, the angle marked with x would be written as CAB or BAC, and the angle marked y would be written as ABC or CBA.

Enter into the boxes below the two different ways of writing the angle marked z in the diagram:

In all the following diagrams, O represents the centre of each circle.

  1. In the following diagram, angle CAB is 74o. Calculate the following angles:

    		ABC = o    
    BCA = o    
    BCD = o    

  2. In the following diagram, L is the mid-point of the chord KM. Angle KOL is 59o. Calculate the size of angle OML.

    OML = o    

  3. In the following diagram AC and BC are chords of the circle, and angle AOD is 47o. Calculate angles OAD and CBO.

    OAD = o    

    CBO = o    

    Enter a single word in the box below to complete the sentence:
    "Lines BC and OD are ."     

  4. In the following diagram, BY is a chord of the circle, XY is a tangent to the circle, and angle BYX is 72o. Calculate angles BYO, YBO and BOY.

    BYO = o    

    YBO = o    

    BOY = o    

  5. In the following diagram, a diameter of the circle starting at P has been extended to meet the tangent QS at Q. The angle ORP is 26o. Calculate the following angles:

    PRS = o    

    OPR = o    

    OQR = o    

    ROQ = o    

  6. In the following diagram (don't you just get bored of hearing that?) the radius OX is parallel to the chord VY, and the line UVW is a tangent. The angle OXV is 56o. Calculate the following angles:

    OVX = o    

    XVW = o    

    VOX = o    

    OVY = o    

    UVY = o    

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