Answered

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Find the measure of the arc or angle indicated. Assume that lines which appeartangent are tangent.Find mMPM12x + 3S45°РRQ3x + 12

Sagot :

Explanation:

The arc MP, arc SQ, and angle MRP are related by the following equation:

[tex]\angle MRP=\frac{1}{2}(MP-SQ)[/tex]

Then, replacing the expressions for each angle and arc, we get:

[tex]3x+12=\frac{1}{2}((12x+3)-45)[/tex]

So, solving for x, we get:

[tex]\begin{gathered} 3x+12=\frac{1}{2}(12x+3-45)_{} \\ 3x+12=\frac{1}{2}(12x-42) \\ 3x+12=\frac{1}{2}(12x)-\frac{1}{2}(42) \\ 3x+12=6x-21 \\ 3x+12+21=6x-21+21 \\ 3x+33=6x \\ 3x+33-3x=6x-3x \\ 33=3x \\ \frac{33}{3}=\frac{3x}{3} \\ 11=x \end{gathered}[/tex]

Now, with the value of x, we get that the measure of arc MP is equal to:

MP = 12x + 3

MP = 12(11) + 3

MP = 132 +3

MP = 135

Therefore, the answer is 135 degr

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