In the following figure, ∆ ABC is an equilateral triangle. Find ∠x.

 

 

Given, ∠DAB = 30°

Since, the measure of each angle of an equilateral triangle is 60°

Therefore, ∠ABC = 60°.

Now, ∠ABD = 180° – 60° = 120° (Linear pair)

In triangle ABD, by angle sum property of a triangle,

∠BAD + ∠ABD + ∠ADB = 180°

30° + 120° + x = 180°

x = 180° – (120° + 30°) = 30°.