Question

HELP PLEASE and show work

Answer 1

Answer:

$\boxed{\stackrel{\Large\frown}{PQS}\:= 222°}$

Explanation:

Since $\overline{PR}$ is a diameter, arc $\stackrel{\Large\frown}{PQR}\:= 180°.$

Given that $\angle{SUR} = 42°$ is a subtended central angle by two diameters,

$\stackrel{\large\frown}{RS} \:= 42°$.

Using the rule of arcs, $\stackrel{\Large\frown}{PQR} + \stackrel{\large\frown}{RS} \: = \: \stackrel{\Large\frown}{PQS}$ →

$180° + \: 42° = \: \stackrel{\Large\frown}{PQS}$

$222° = \: \stackrel{\Large\frown}{PQS}$

$\stackrel{\Large\frown}{PQS} \: = \: 222°$