find measure of arc from inscribed angle
Check the final answer first, then review the worked steps.
Problem
find measure of arc from inscribed angle
Answer
\(64^\circ\)
Step-by-step solution
- Identify the geometric components: The problem shows a circle with points $J$, $K$, and $L$ on its circumference. We are given an inscribed angle $\angle JKL$ with a measure of $32^\circ$. We need to find the measure of the intercepted arc $\overset{\frown}{JL}$.
- Apply the Inscribed Angle Theorem: The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Mathematically, this is expressed as: $m\angle JKL = \frac{1}{2} m\overset{\frown}{JL}$.
- Calculate the arc measure: We are given $m\angle JKL = 32^\circ$. Substituting this into the formula: $32^\circ = \frac{1}{2} m\overset{\frown}{JL}$. To solve for $m\overset{\frown}{JL}$, multiply both sides of the equation by $2$: $m\overset{\frown}{JL} = 32^\circ \times 2 = 64^\circ$.