Respuesta :

  • Angle p=Angle R=2x+19

According to angle sum property

[tex]\\ \sf\longmapsto x+17+2x+19+6x-5+2x+19=360[/tex]

[tex]\\ \sf\longmapsto x+2x+6x+2x+17+19+19-5=360[/tex]

[tex]\\ \sf\longmapsto 11x+50=360[/tex]

[tex]\\ \sf\longmapsto 11x=360-50[/tex]

[tex]\\ \sf\longmapsto 11x=310[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{310}{11}[/tex]

[tex]\\ \sf\longmapsto x\approx 28[/tex]

Now

[tex]\\ \sf\longmapsto <ROP=x+17[/tex]

[tex]\\ \sf\longmapsto 28+17=45[/tex]

mhanifa

Answer:

  • 41°

Step-by-step explanation:

Since the OPQR is cyclic quadrilateral its opposite angles are supplementary.

Find the value of x first:

  • m∠ROP + m∠RQP = 180
  • x + 17 + 6x - 5 = 180
  • 7x = 180 - 12
  • 7x = 168
  • x = 168/7
  • x = 24

Find the angle ROP:

  • 24 + 17 = 41°

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