Given:
Given that the measure of arc MN is (9x - 43)°
The measure of arc NP is (5x + 33)°
We need to determine the measure of arc MP
Value of x:
From the figure, it is obvious that MN is perpendicular to R and NP is perpendicular to R, then their chords are congruent.
Since, the chords are congruent, then their arcs MN and NP are congruent.
Thus, we have;
[tex]9x-43=5x+33[/tex]
[tex]4x-43=33[/tex]
[tex]4x=76[/tex]
[tex]x=19[/tex]
Thus, the value of x is 19.
Measure of arcs MN and NP:
The measures of arcs MN and NP can be determined by substituting x = 19.
Thus, we have;
[tex]MN=(9(19)-43)^{\circ}=(171-43)^{\circ}=128^{\circ}[/tex]
[tex]NP=(5(19)+33)^{\circ}=(95+33)^{\circ}=128^{\circ}[/tex]
Thus, the measure of arc MN is 128° and the measure of arc NP us 128°
Measure of arc MP:
The measure of arc MP is given by
[tex]m \widehat{MP}=360^{\circ}-128^{\circ}-128^{\circ}[/tex]
[tex]m \widehat{MP}=360^{\circ}-256^{\circ}[/tex]
[tex]m \widehat{MP}=104^{\circ}[/tex]
Thus, the measure of arc MP is 104°
