Question

Find x.

A)4
B)6.7
C)7.2
D)9

Answer 1

@Walleye can you help me ?

Answer 2

im trying but I cant seem to think of how to get the answer

Answer 3

my brain is farting

Answer 4

@taewony can you help me ?

Answer 5

ABCD is a cyclic quadrilateral, so:\[
\begin{align}
\angle BCD+\angle BAD&=180^0\\
\text{but }\angle BAP+\angle BAD&=180^0\\
\therefore \angle BAP&=\angle BCD&=\alpha\\
\text{similarly, we can show:}\\
\angle ABP &= \angle ADC&=\beta\\
\text{now, using the sine rule we get:}\\
\text{in }\triangle PAB\frac{3}{\sin(\alpha)}&=\frac{4}{\sin(\beta)}\tag{1}\\
\text{in }\triangle PDC\frac{5+4}{\sin(\alpha)}&=\frac{3+x}{\sin(\beta)}\tag{2}\\
\text{dividing (1) by (2) we get:}\\
\frac{3}{5+4}=\frac{4}{3+x}\\
\therefore 9+3x=36\\
\therefore 3x=27\\
\therefore x=9
\end{align}\]