Question

Find the value of x. Then classify the triangle by its angle measures.

Short answer

The value of x is$x=63°$ and the triangle is a scalenetriangle.

Step-by-step solution

Step 1. Given Information.

One angle of the triangle is$x°$.

Second angle is given as$\left(x+15\right)°$.

Third angle is given as$39°$.

Step 2. Formula.

Sum of all angles of a triangle is$180°$.

Step 3. Calculation.

The sum of all the angles of a triangle is$180°$.

This gives us-

$\begin{array}{c}x°+\left(x+15\right)°+39=180°\\ x°+x°+15°+39°=180°\end{array}$

Add both the x and the numbers.

$2x{}^{\circ }+54{}^{\circ }=180°$

Subtract 54 from both the sides.

$2x{}^{\circ }+54{}^{\circ }-54{}^{\circ }=180{}^{\circ }-54°$

This gives us,

$2x{}^{\circ }=126°$

Now, divide both sides by 2.

$\frac{2x°}{2}=\frac{126°}{2}$

This will give us the value of x.

$x=63°$

The first angle of the triangle is given as $x°$ and the value of x is$x=63°$.

The second angle of the triangle is given as$\left(x+15\right)°$.

To find the value of the angle, add 63 and 15.

$63{}^{\circ }+15{}^{\circ }=78°$

So, the third angle is$78°$.

Step 4. Conclusion.

The value of x is$x=63°$.

One angle is$63°$, second angle is $78°$and the third angle is$39°$.

All the three angles of the triangle are different. Hence, it is a Scalene triangle.