Question

In the given figure, AB = AD and BCD = 120°. Find the measure of angle ADB. please teach me step by step​

Answer 1

Answer:

 The answer will be ∠ADB = 60°.

Step-by-step explanation:

Given things are;

AB = AD

 ∠BCD = 120°

Opposite angles of the quadrilateral inscribed inside a circle add up to make 180°. (Its a theorem you should know about an inscribed quadrilateral.)

Thus,  ∠BCD +  ∠BAD = 180°

120° + ∠BAD = 180°

 ∠BAD = 60°. (iii)

Now, angles opposite to two equal sides of a triangle (isosceles triangle) are equal. (Its also a theorem you should know about an isosceles triangle.)

Hence,  ∠ABD = ∠ADB. (i)

Now, using angle sum property of a triangle, we can deduce;

∠ABD + ∠ADB + ∠BAD = 180° (ii)

Angle sum property of a triangle states that sum of all the angles of a triangle will equal to 180°.

Using equation (i) and (ii), it can be deduced that;

∠ADB + ∠ADB + ∠BAD = 180°;

2∠ADB + ∠BAD = 180°;

2∠ADB + 60° = 180°; (∠BAD = 60° eq.(iii))

2∠ADB = 180 - 60;

∠ADB = 120/2;

∠ADB = 60°.

Therefore, ∠ADB = 60°.

That's all.