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We are not looking for a solution. We are confused by the wording and need help with the diagram. Then we can solve the problem on our own.

Here is the exercise in the text.

A surveyor is measuring the length of a lake. He takes angle measurements from two positions, $A$ and $B$, that are 136 m apart and on the same side of the lake. From $B$, the measure of the angle between the sight lines to the ends of the lake is $130^\circ$, and the measure of the angle between the sight lines to $A$ and one end of the lake is $120^\circ$. From $A$, the measure of the angle between the sight lines to the ends of the lake is $65^\circ$, and the measure of the angle between the sight lines to $B$ and the same end of the lake is $20^\circ$. Calculate the length of the lake, to the nearest metre.

Here is our diagram. What angles are $120^\circ$ and $20^\circ$?

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1 Answer

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Here's a possibility: The "ends" of the lake are points $C$ and $D$; $\angle CBD=130^\circ$, $\angle DBA=120^\circ$, $\angle CAD=65^\circ$, $\angle BAD=20^\circ$.

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