Question

PLEASE HELP ! Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?

Answer 1

• Angle p=Angle R=2x+19

According to angle sum property

$\\ \sf\longmapsto x+17+2x+19+6x-5+2x+19=360$

$\\ \sf\longmapsto x+2x+6x+2x+17+19+19-5=360$

$\\ \sf\longmapsto 11x+50=360$

$\\ \sf\longmapsto 11x=360-50$

$\\ \sf\longmapsto 11x=310$

$\\ \sf\longmapsto x=\dfrac{310}{11}$

$\\ \sf\longmapsto x\approx 28$

Now

$\\ \sf\longmapsto$

$\\ \sf\longmapsto 28+17=45$

Answer 2

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°