Question

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

Short answer

The value of x is$x=49°$ and the triangle is a scalene right-angled triangle.

Step-by-step solution

Step 1. Given Information.

One angle of the triangle is$49°$.

Second angle is given as$41°$.

Third angle is given as$\left(2x-8\right)°$.

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,

$\left(2x-8\right){}^{\circ }+49{}^{\circ }+41{}^{\circ }=180°$

Add both numbers together.

$\left(2x-8\right){}^{\circ }+90{}^{\circ }=180°$

Subtract 90 from both the sides.

$\left(2x-8\right){}^{\circ }+90{}^{\circ }-90{}^{\circ }=180{}^{\circ }-90°$

This gives us,

$\left(2x-8\right){}^{\circ }=90°$

Now, add both sides with 8

$2x{}^{\circ }-8{}^{\circ }+8{}^{\circ }=90{}^{\circ }+8°$

This gives us,

$2x{}^{\circ }=98°$

Now, divide both sides by 2.

$\frac{2x°}{2}=\frac{98°}{2}$

This will give us the value of x.

$x=49°$

Since, the third angle of the triangle is given as$\left(2x-8\right)°$.

To find the value of the angle, multiply 2 with 49 and then subtract 8 from it.

$2\times 49{}^{\circ }-8{}^{\circ }=90°$

So, the third angle is$90°$.

Step 4. Conclusion.

The value x is$x=49°$.

One angle is$49°$, second angle is $41°$and the third angle is$90°$.

All the three angles of the triangle are different. Hence, it is a scalene right-angled triangle.