Question

Find the measure of the arc or angle indicated.​

Answer 1

For each problem, use the inscribed angle theorem.

19.

`45^\circ=\frac12m\widehat{QR}\implies m\widehat{QR}=90^\circ`

20.

`95^\circ=\frac12m\widehat{ABC}\implies m\widehat{ABC}=190^\circ`

21.

`49^\circ=\frac12m\widehat{LR}\implies m\widehat{LR}=98^\circ`

LN is a diameter, so arc LN has measure 180º, and so

`m\widehat{LR}+m\widehat{RN}=m\widehat{LN}=180^\circ\implies m\widehat{RN}=82^\circ`