Question

in circle j with $m\angle hlk = 43^\circ$, find the measure of minor arc $\overset{\frown}{hk}$.

Explanation:

Step1: Identify angle type

$\angle HLK$ is an inscribed angle intercepting arc $\overset{\frown}{HK}$.

Step2: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So, $m\angle HLK = \frac{1}{2}m\overset{\frown}{HK}$.

Step3: Solve for arc measure

Rearrange the formula: $m\overset{\frown}{HK} = 2 \times m\angle HLK$. Substitute $m\angle HLK = 43^\circ$:
$m\overset{\frown}{HK} = 2 \times 43^\circ$

Answer:

$86^\circ$