Given that NL and MK are diameters of circle J, …

Mathematics Questions

NL and MK are diameters of circle J. Complete the statements about circle J. MP is a major arc/minor arc and measures __ degrees. MLN is a minor arc/major arc/semicircle and measures __ degrees.

Short Answer

The analysis of arcs MP and MLN within circle J reveals that arc MP measures 152° and is classified as a minor arc, while arc MLN measures 298° and is classified as a major arc.

Step-by-Step Solution

Step 1: Identify the Arcs and Their Sizes

In this scenario, we are analyzing two arcs, MP and MLN, within circle J. To determine their respective measurements, we first consider the size of arc MP. It is calculated by adding the angles at points M and P, which gives us:

  • MP = 62¬¨‚àû + 90¬¨‚àû = 152¬¨‚àû

Step 2: Classify Arc MP

Based on the calculated size of arc MP, we can classify it as a minor arc. Minor arcs are defined as those that measure less than 180°. Since the measure of MP is 152°, it fulfills that criterion. Thus, the specifics for MP are:

  • MP is a minor arc
  • Measures 152¬¨‚àû

Step 3: Analyze and Classify Arc MLN

Next, we evaluate arc MLN by using the full circle’s measurement of 360¬¨‚àû. The size of arc MLN can be determined by subtracting the size of arc MP from the total degrees in a circle:

  • MLN = 360¬¨‚àû – 62¬¨‚àû = 298¬¨‚àû

Since this measurement exceeds 180°, arc MLN is classified as a major arc. The descriptions for MLN are:

  • MLN is a major arc
  • Measures 298¬¨‚àû

Related Concepts

Arc

A portion of the circumference of a circle defined by two endpoints and the continuous line connecting them

Minor Arc

An arc that measures less than 180°

Major Arc

An arc that measures more than 180°

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