Question

Find the measure of the arc or angle indicated.​

Answer 1

For each problem, use the inscribed angle theorem.

19.

$45^\circ=\dfrac12m\widehat{QR}\implies m\widehat{QR}=90^\circ$

20.

$95^\circ=\dfrac12m\widehat{ABC}\implies m\widehat{ABC}=190^\circ$

21.

$49^\circ=\dfrac12m\widehat{LR}\implies m\widehat{LR}=98^\circ$

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

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