In a trapezium ABCD with AB || DC, AB = 17 cm, AD = 16 cm, and angle ABC = 150 degrees. Given AB = BD = 17 cm, find the length of BC.

Here's the solution to the problem:

a) The length of BC

Step 1: Identify known values and properties.
We are given $AB = 17$ cm, $AD = 16$ cm, $\angle ABC = 150^\circ$.
We are also given that $AB = BD = 17$ cm. This means $\triangle ABD$ is an isosceles triangle.
Since $AB \parallel DC$, $ABCD$ is a trapezium.

Step 2: Calculate $\angle ABD$ using the Cosine Rule in $\triangle ABD$.
In $\triangle ABD$, sides are $AB=17$, $BD=17$, $AD=16$.

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