Question

the measures of the angles of a triangle are shown in the figure below find the measure of the smallest angle(3x-9)°(x+15)°90

Answer 1

The sum of the angles of a triangle is equal to 180 degree.

Determine the value of x by sum of angles of triangle.

$\begin{gathered} (3x-9)+(x+15)+90=180 \\ 3x-9+x+15+90=180 \\ 4x=180-96 \\ x=\frac{84}{4} \\ =21 \end{gathered}$

Determine the measure of the angles.

$\begin{gathered} 3x-9=3\cdot21-9 \\ =63-9 \\ =54 \end{gathered}$$\begin{gathered} x+15=21+15 \\ =36 \end{gathered}$

Thus, the value of x is 21 and measure of smallest angle is 36 degree.