Given a line BC and a point A on it, construct a ray AD using set squares so that ∠DAC is

(i) 30°
(ii)60°

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Solution

(i) Draw a line BC and take a point A on it. Place 30° set-square on the line BC such that its vertex of 30° angle lies on point A and one edge coincides with the ray AC as shown in the figure.
Draw the ray AD.

Thus, $∠$ DAC is the required angle of 30°.

(ii) Draw a line BC and take a point A on it. Place 30° set-square on the line BC such that its vertex of 30° angle lies on point A and one edge coincides with the ray AB as shown in the figure.
Draw the ray AD.

$∠$ DAB = 30°
We know that the angles an one side of the straight line will always add to 180°.
∴ $∠$ DAB + $∠$ DAC = 180°
30° + $∠$ DAC = 180°
$∠$ DAC = 180° − 30°
∴ $∠$ DAC = 150°

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