Question

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

Answer 1

84.30°

Step-by-step explanation

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

`m\angle RST=m\angle RSU+m\angle UST`

Substitute the known values or expressions,

`13x+5=78+3x-12`

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,

`\begin{gathered} 13x+5=(78-12)+3x \\ \\ 13x+5=66+3x \end{gathered}`

Subtract 3x and 5 from both sides,

`\begin{gathered} 13x-3x+5-5=66-5+3x-3x \\ \\ 10x=61 \end{gathered}`

And divide both sides by 10,

`\begin{gathered} (10x)/(10)=(61)/(10) \\ \\ x=6.1 \end{gathered}`

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

`m\angle RST=13x+5=13\cdot6.1+5=79.30+5=84.30`

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