Question

determine the measure of the inscribed angle (you may have to go to tenths place) (1 decimal point)
m\widehat{rt}=140^{circ}
\angle rst =
\angle jkl =

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.

Step2: Calculate \(\angle RST\)

Given \(m\widehat{RT}=140^{\circ}\). By the inscribed - angle theorem, \(\angle RST=\frac{1}{2}m\widehat{RT}\).
Substitute \(m\widehat{RT} = 140^{\circ}\) into the formula: \(\angle RST=\frac{1}{2}\times140^{\circ}=70^{\circ}\).

Step3: Calculate \(\angle JKL\)

Given \(m\widehat{JL}=15^{\circ}\). By the inscribed - angle theorem, \(\angle JKL=\frac{1}{2}m\widehat{JL}\).
Substitute \(m\widehat{JL}=15^{\circ}\) into the formula: \(\angle JKL=\frac{1}{2}\times15^{\circ}=7.5^{\circ}\).

Answer:

\(\angle RST = 70^{\circ}\), \(\angle JKL=7.5^{\circ}\)