Question

ABCD is a quadrilateral Work out angle x​

Answer 1

First of all, we can work out the length of BD: using the pythagorean theorem, we have

$BD = \sqrt{6^2+8^2}=10$

Now, we can work on triangle BCD and use the sine theorem: we have

$\dfrac{BD}{\sin(\hat{C})} = \dfrac{CD}{\sin(x)}$

Plugging the values and solving for $\sin(x)$ we have

$\dfrac{10}{\sin(29)} = \dfrac{13}{\sin(x)} \iff \sin(x)=\dfrac{13\cdot \sin(29)}{10}\approx 0.63$

We deduce

$x=\arcsin(0.63)\approx 39$