Question

find angle BAD of the diagram.​

Answer 1

Answer:

$∠BAD≈65.22°$

Step-by-step explanation:

Note:

The following formula is tan formula:

$tan(\theta)=\dfrac{opposite}{adjacent}$

1) Finding the tan of ∠BAC

$tan(\theta)=\dfrac{4}{5}$

$\theta=tan^-1(\dfrac{4}{5})$

2) Finding the tan of ∠CAD

$tan(\theta)=\dfrac{3}{6}$

$\theta=tan^-1(\dfrac{3}{6})$

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

$tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{3}{6})≈65.22°$

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

Then

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

$tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{5}{4})+tan^-1(\dfrac{3}{6})+tan^-1(\dfrac{6}{3})=180°$

$180°+∠CDA+∠CBA=^?360$

$180°+90°+90°=^?360°$

$360°=360°$