Question

the total measure of the three angles of a triangle are 4×-1, 3x + 7 and 9x-15 what is the measure of the largest angle?

Answer 1

It is important to note that the sum of the measures of the interior angles of a triangle is 180°.

Based on the question, 4x - 1, 3x + 7, and 9x - 15 are the measures of the 3 angles of a triangle. Therefore, adding these three measures must sum up to 180°.

`(4x-1)+(3x+7)+(9x-15)=180`

From the three angles mentioned, we don't know yet which one is the largest. For us to know, we need to get the value of x first.

So, to get the value of x, we can use the equation we wrote above.

`\begin{gathered} \text{Eliminate the parenthesis.} \\ 4x-1+3x+7+9x-15=180 \\ \text{Combine similar terms.} \\ 16x-9=180 \\ \text{Add 9 on both sides.} \\ 16x-9+9=180+9 \\ 16x=189 \\ \text{Divide both sides by 16.} \\ (16x)/(16)=(189)/(16) \\ x=11.8125 \end{gathered}`

Now that we have the value of x, let's plug this in to the 3 measures of angles and see which one is the largest.

`4x-1=4(11.8125)-1=47.25-1=46.25`
`3x+7=3(11.8125)+7=35.4375+7=42.4375`
`9x-15=9(11.8125)-15=106.3125-15=91.3125`

Therefore, the measure of the largest angle is 91.3125° or 91.31° when rounded off to the nearest hundredth.