Question

Find angle BAD of the diagram.​

Answer 1

`∠BAD≈65.22°`

Explanation:

Note:

The following formula is tan formula:

`tan(\theta)=(opposite)/(adjacent)`

1) Finding the tan of ∠BAC

`tan(\theta)=(4)/(5)`

`\theta=tan^-1((4)/(5))`

2) Finding the tan of ∠CAD

`tan(\theta)=(3)/(6)`

`\theta=tan^-1((3)/(6))`

3) Add the value of ∠BAC to the value of ∠CAD

`tan^-1((4)/(5))+tan^-1((3)/(6))≈65.22°`

4) The sum of interior angles in quadrilateral is 360°

Then

`tan(∠BAC)+tan(∠ACB)+tan(∠CAD)+tan(∠ACD)=360°`

`tan^-1((4)/(5))+tan^-1((5)/(4))+tan^-1((3)/(6))+tan^-1((6)/(3))=180°`

`180°+∠CDA+∠CBA=^?360`

`180°+90°+90°=^?360°`

`360°=360°`