Question

I need help finding mMP

Answer 1

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;

$9x-43=5x+33$

$4x-43=33$

       $4x=76$

         $x=19$

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;

$MN=(9(19)-43)^{\circ}=(171-43)^{\circ}=128^{\circ}$

$NP=(5(19)+33)^{\circ}=(95+33)^{\circ}=128^{\circ}$

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

$m \widehat{MP}=360^{\circ}-128^{\circ}-128^{\circ}$

$m \widehat{MP}=360^{\circ}-256^{\circ}$

$m \widehat{MP}=104^{\circ}$

Thus, the measure of arc MP is 104°