Question

if ( mangle mpl = 63^{circ} ), find each measure.

1. ( mwidehat{jk}=27^{circ} )
2. ( mwidehat{nj}=square^{circ} )
3. ( mwidehat{jl}=117^{circ} )
4. ( mwidehat{knm}=square^{circ} )
5. ( mwidehat{mjl}=square^{circ} )
6. ( mwidehat{jlk}=square^{circ} )

Explanation:

Step1: Find the measure of \(m\angle JPN\)

Since the sum of angles around a point \(P\) is \(360^{\circ}\), and we know \(m\angle MPL = 63^{\circ}\), \(m\angle KPL=90^{\circ}\) (right - angle), \(m\angle JPK = 27^{\circ}\) (from problem 4).
First, find \(m\angle JPN\):

$$360-(90 + 63+27+27)=153^{\circ}$$

Step2: Calculate \(m\overarc{NJ}\)

The measure of an arc is equal to the measure of its central angle. So \(m\overarc{NJ}=m\angle JPN = 153^{\circ}\)

Answer:

\(153\)