1 Answer

Wonsuc · Answer 1 · 2022-03-26T00:11:56+0000

Answer:

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

Step-by-step 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,
$\stackrel{\Large\frown}{PQR} + \stackrel{\large\frown}{RS} \: = \: \stackrel{\Large\frown}{PQS}$ →

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

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

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

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