Question
Given a line $BC$ and a point $A$ on it, construct a ray $AD$ using set squares so that $\angle\text{DAC}$ is: $150^\circ $
✓
Answer
Draw a line $BC$ and take a point $A$ on it.
Place $30^\circ $ set-square on the line $BC$ such that its vertex of $30^\circ $ angle lies on point A and one edge coincides with the ray $AB$ as shown in the figure. Draw the ray $AD.$
Therefore, $\angle\text{DAB}=30^{\circ}$
We know that angle on one side of the straight line will always add to $180^\circ $
Therefore, $\angle\text{DAB}+\angle{\text{DAC}}=180^{\circ}$
Therefore, $\angle\text{DAC}=150^{\circ}$
Place $30^\circ $ set-square on the line $BC$ such that its vertex of $30^\circ $ angle lies on point A and one edge coincides with the ray $AB$ as shown in the figure. Draw the ray $AD.$
Therefore, $\angle\text{DAB}=30^{\circ}$
We know that angle on one side of the straight line will always add to $180^\circ $
Therefore, $\angle\text{DAB}+\angle{\text{DAC}}=180^{\circ}$
Therefore, $\angle\text{DAC}=150^{\circ}$
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