Question

8) The measure of three angles of a triangle are xº,(x +29) ° and (x - 5)º. Find the measures of all threeangles. (3 pts)

Answer 1

Let's name each of them:

$\begin{gathered} a=xº \\ b=(x+29)º \\ c=(x-5)º \end{gathered}$

The sum of the angles of a triangle is always equal to 180º, so:

$\begin{gathered} a+b+c=180º \\ xº+(x+29)º+(x-5)º=180º \\ x+x+29+x-5=180 \\ 3x+24=180 \\ 3x=180-24 \\ 3x=156 \\ x=\frac{156}{3} \\ x=52 \end{gathered}$

Now that we know tha value of x, we can find the values of all three angles:

$\begin{gathered} a=52º \\ b=(52+29)º=81º \\ c=(52-5)º=47º \end{gathered}$