a) Work out the size of AOD.

b) Work out the size of angle ABC and give a reason for your answer.

Thanks in advance :)

Angle AOC and ABC have the angle theorem: the angle subtended at the centre of the circle is double the angle at the circumference. Its quite hard to realise the layout, because angle AOC isn't between points A and C. If angle AOC moved to the right side of line AB, it would be easier to see. Of course we cannot do this, otherwise angle AOC wouldn't be the middle anymore. Hope this helped

ibiscollingwood ibiscollingwood · Answer 2 · 2022-02-03T13:48:19+01:00

(a). The angle AOD is 62 degrees.

(b). The angle ABC is 31 degrees.

(a). From given diagram, It is observed that triangle AOD is a right angle triangle.

The sum of all three angles in triangle is equal to 180 degrees.

[tex]\angle A +\angle O + \angle D = 180\\\\90 +\angle AOD +28=180\\\\\angle AOD=180-90-28=62[/tex]

(b). The central angle theorem states that the angle subtended by an arc at the center of the circle is double the angle subtended at any point on the circumference of the circle.

[tex]\angle ABC = \frac{1}{2} \angle AOD\\ \\\angle ABC=\frac{1}{2}*62=31[/tex]

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a) Work out the size of AOD.b) Work out the size of angle ABC and give a reason for your answer.Thanks in advance :)

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a) Work out the size of AOD.

b) Work out the size of angle ABC and give a reason for your answer.

Thanks in advance :)