Question

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

Explanation:

Step1: Recall inscribed - angle theorem

In a circle, inscribed angles that intercept the same arc are equal. So, $\angle KJL=\angle KML$.
$$7x - 8=3x + 8$$

Step2: 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: $x = 4$.

Step3: Find the measure of $\angle KML$

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

Step4: Find the measure of arc $KL$

The measure of an arc is twice the measure of the inscribed - angle that intercepts it. So the measure of arc $KL = 2\angle KML$.
$$\text{Measure of arc }KL=2\times20^{\circ}=40^{\circ}$$

Answer:

$40^{\circ}$