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The measure of /RST can be represented by the expression (13x + 5)°What is m/RST rounded to the nearest hundredth? (ex 80.501

The Measure Of RST Can Be Represented By The Expression 13x 5What Is MRST Rounded To The Nearest Hundredth Ex 80501 class=

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ANSWER

84.30°

EXPLANATION

By the angle addition theorem, the measure of angle RST is,

[tex]m\angle RST=m\angle RSU+m\angle UST[/tex]

Substitute the known values or expressions,

[tex]13x+5=78+3x-12[/tex]

To find the measure of angle RST we have to find the value of x first. Add like terms on the right side of the equation,

[tex]\begin{gathered} 13x+5=(78-12)+3x \\ \\ 13x+5=66+3x \end{gathered}[/tex]

Subtract 3x and 5 from both sides,

[tex]\begin{gathered} 13x-3x+5-5=66-5+3x-3x \\ \\ 10x=61 \end{gathered}[/tex]

And divide both sides by 10,

[tex]\begin{gathered} \frac{10x}{10}=\frac{61}{10} \\ \\ x=6.1 \end{gathered}[/tex]

Now, knowing the value of x, we can substitute this value into the expression for the measure of angle RST,

[tex]m\angle RST=13x+5=13\cdot6.1+5=79.30+5=84.30[/tex]

Hence, the measure of angle RST is 84.30°, rounded to the nearest hundredth.

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