Question

I need to know if it’s A B C OR D

Answer 1

Consider the property, opposite angle of a cyclic quadrilateral are supplementary

hence

`\angle NMP+\angle NOP=180^0`

Recall that

`\begin{gathered} \angle NMP=\angle M=(8x-24)^0 \\ \text{and } \\ \angle NOP=\angle O=(4x)^0 \end{gathered}`

Hnece, we have that

`\begin{gathered} \angle M+\angle O=180^0(opposite\text{ angles of a cyclic quadrilateral)} \\ (8x-24)^0+4x^0=180^0 \end{gathered}`

Then

`\begin{gathered} 8x-24+4x=180 \\ 8x+4x-24=180 \\ 12x-24=180 \\ \text{Add 24 t o both sides } \\ 12x-24+24=180+24 \\ 12x=204 \\ \text{divide both sides by 12} \\ (12x)/(12)=(204)/(12) \\ \text{Then} \\ x=17 \end{gathered}`

Hence

x=17

Since

`\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4*17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}`

Therefore

The measure of angle NOP is 68⁰

Answer; 68⁰ (The fourth Option )