Question

In the figure, ∠ABD=3 ∠DAB and ∠BDC=96°. Find ∠ABD.

Answer 1

Dear Student,

Answer : angle ABD = 24°

Solution: please find the entire solution in the attachment.

Hint: First solve angle ADB ,after that apply the sum of interior angle of triangle is equal to 180°

Hope you understand well by looking attached image.

Answer 2

*********************************"*************

Theorem ;

If a side of a triangle is produced, then

the exterior angle so formed is equal to

the sum of the interior opposite angles.

*****************************************************

Here ,

In ∆ ABD , AD side is produced to C,

Exterior angle BDC = 96°

interior opposite angles are <DAB,and

<ABD .

Let <DAB = x° ,

<ABD = 3x° ( given )

Therefore ,

Sum of interior opposite angles =Exterior

angle <BDC

<DAB + <ABD = exterior angle <BDC

x + 3x = 96°

4x = 96°

x = 96°/4

x° = 24

Therefore ,

<DAB = x° = 24°

<ABD = 3x

= 3 × 24°

= 72°

I hope this helps you.

: )