Question

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

Explanation:

Step1: Set angles equal (inscribed angles)

Angles subtended by the same arc are congruent, so:
$$7x - 8 = 3x + 8$$

Step2: Solve for x

Rearrange to isolate x:
$$7x - 3x = 8 + 8$$
$$4x = 16$$
$$x = \frac{16}{4} = 4$$

Step3: Find inscribed angle measure

Substitute x into one angle formula:
$$7(4) - 8 = 28 - 8 = 20^\circ$$

Step4: Calculate arc KL

Arc measure = 2×inscribed angle:
$$2 \times 20^\circ = 40^\circ$$

Answer:

40°