Question

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

Explanation:

Step1: Find the measure of \(\overarc{MP}\)

• \(\overarc{MP}\) is an arc.
• The central angle for \(\overarc{MP}\) is \(\angle MJN+\angle NJP\).
• Given \(\angle MJN = 62^{\circ}\) and \(\angle NJP=90^{\circ}\).
• So, \(\angle MJP=62^{\circ}+90^{\circ}=152^{\circ}\).
• Since \(\overarc{MP}\) is a major arc (an arc greater than a semicircle) with measure equal to the central angle subtended by it.

Step2: Find the measure of \(\overarc{MLN}\)

• \(\overarc{MLN}\) is a semicircle.
• The measure of a semicircle is \(180^{\circ}\) as the central angle for a semicircle is \(180^{\circ}\) (diameter subtends a \(180^{\circ}\) angle at the center of a circle).

Answer:

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