Question

HELP PLEASE and show work

Answer 1

`\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°`