Question

In the figure AB = 10 cm, ∠B = 30°, DC = 5 cm

angle θ = ______. 

Options

• 30°

• 45°

• 60°

• none of these

Answer 1

angle θ = 45°. 

Explanation:

In △ABD,

AD = AB ⋅ sin 30° = 10 × 21 ​= 5 cm

and given DC = 5cm

In △ADC,

AD = DC = 5 cm 

so it is an isosceles right-angled triangle (right angle at D)

θ = ∠ACD = 45°