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Alex73 [517]
3 years ago
5

What is the value of s ?

Mathematics
2 answers:
Stells [14]3 years ago
8 0
25 degrees : 63 - 38 to get s
horrorfan [7]3 years ago
6 0

Answer:

25 degrees

Step-by-step explanation:

vertical angle 63 make oposite lines form a 63 degree angle. You need to find s. Now subtract 38 from 63, so 63-38 = 25 degrees

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SOLUTION

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} \\ \frac{12x}{12}=\frac{204}{12} \\ \text{Then} \\ x=17 \end{gathered}

Hence

x=17

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\begin{gathered} \angle NOP=(4x)^0 \\ \text{substitute the value of x, we have } \\ \angle NOP=4\times17=68^0 \\ \text{Hence } \\ \angle NOP=68^0 \end{gathered}

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The measure of angle NOP is 68⁰

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