angle kjl measures (7x - 8)°. angle kml measures (3x + 8)°. what is the measure of arc kl? 20° 40° 48° 96°

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Angles $\angle KJL$ and $\angle KML$ intercept the same arc $\overset{\frown}{KL}$. So, $\angle KJL=\angle KML$.

Step2: Set up the equation

Set $7x - 8=3x + 8$.

Step3: Solve the equation for $x$

Subtract $3x$ from both sides: $7x-3x - 8=3x-3x + 8$, which simplifies to $4x-8 = 8$. Then add 8 to both sides: $4x-8 + 8=8 + 8$, so $4x=16$. Divide both sides by 4: $x = 4$.

Step4: Find the measure of $\angle KML$

Substitute $x = 4$ into the expression for $\angle KML$: $\angle KML=(3x + 8)^{\circ}=(3\times4 + 8)^{\circ}=(12 + 8)^{\circ}=20^{\circ}$.

Step5: Find the measure of arc $\overset{\frown}{KL}$

Since the measure of an inscribed angle is half the measure of its intercepted arc, if $\angle KML = 20^{\circ}$, then the measure of arc $\overset{\frown}{KL}=2\times\angle KML$. So, the measure of arc $\overset{\frown}{KL}=40^{\circ}$.

Answer:

$40^{\circ}$