Question

finding arc measures
nl and mk are diameters of circle j.
complete the statements about circle j.
mp is a and measures degrees.
mln is and measures degrees.

Explanation:

Step1: Determine the type and measure of arc \( \overarc{MP} \)

• A minor arc is an arc that is less than a semicircle.
• The measure of an arc is equal to the measure of its central angle.
• The central angle for \( \overarc{MP} \) is \( 62^{\circ}+90^{\circ}=152^{\circ}\). Since \( 152^{\circ}<180^{\circ}\), \( \overarc{MP} \) is a minor arc and measures \( 152^{\circ}\).

Step2: Determine the type and measure of arc \( \overarc{MLN} \)

• A semicircle is an arc that measures \( 180^{\circ}\).
• Since \( \overline{NL} \) is a diameter of the circle \( J \), the arc \( \overarc{MLN} \) is a semicircle and measures \( 180^{\circ}\).

Answer:

\( \overarc{MP} \) is a minor arc and measures \( 152 \) degrees. \( \overarc{MLN} \) is a semicircle and measures \( 180 \) degrees.