Answer
$\angle$1=39$^{\circ}$
$\angle$4=39$^{\circ}$
$\angle$2=51$^{\circ}$
$\angle$3=51$^{\circ}$
$\angle$5=39$^{\circ}$
$\angle$6=39$^{\circ}$
Work Step by Step
Given:
$\overline{UZ}$$\parallel$$\overline{XZ}$
$\overline{VY}$$\bot$$\overline{UW}$
$\overline{VY}$$\bot$$\overline{XZ}$
lets find the value of x
according to the figure and question its is clear that
$\angle$1=$\angle$4 and
$\angle$2=$\angle$3
and
$\angle$1+$\angle$4+$\angle$2+$\angle$3= 180$^{\circ}$
so,
4x+3+4x+3+6x-3+6x-3=180
20x=180
x=9
therefore,
$\angle$1=$\angle$4=4(9)+3=39$^{\circ}$
$\angle$2=$\angle$3=6(9)-3=51$^{\circ}$
and
$\angle$5=39$^{\circ}$ and $\angle$6=39$^{\circ}$ because both are alternate angles of $\angle$1 and $\angle$4 respectively.
