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This is a practice assessment not for a grade! I just need help understanding it and the answer to be able to have an example to look back to

This is a practice assessment not for a grade! I just need help understanding it and-example-1

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\angle MP=64^0

And it is the angle at the centre of a circle

The theorem,

Angle at the centre of a circle = 2 x angle at the other part of the circumference

Hence;


\begin{gathered} \angle MP\text{ = 2 x }\angle N \\ 64^0=2\text{ x }\angle N \end{gathered}

Divide both sides by 2


\begin{gathered} \angle N=(64)/(2) \\ \angle N=32^0 \end{gathered}

Part B:

We are to find the angle at the centre in this case

The angle at the centre is NQ and P is the angle at the circumference

Applying the same theorem as we used in part A, that is

Angle at the centre of a circle = 2 x angle at the other part of the circumference


\begin{gathered} \angle NQ\text{ = 2 x }\angle P \\ \angle NQ\text{ = 2 x 53} \\ \angle NQ=106^0 \end{gathered}

Hence, angle N = 32 degrees and angle NQ = 106 degrees.

User VMois
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