Question

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

Short answer

The value of x is$x=65°$, and the triangle is a scalene right-angled triangle.

Step-by-step solution

Step 1. Given Information.

One angle of the triangle is$25°$.

Second angle is given as$x°$.

Third angle is given as$\left(x+25\right)°$.

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,

$x+\left(x+25\right){}^{\circ }+25{}^{\circ }=180°$

Add both x and both numbers together.

$2x+50{}^{\circ }=180°$

Subtract 50 from both the sides.

$2x+50{}^{\circ }-50{}^{\circ }=180{}^{\circ }-50°$

This gives us,

$2x=130°$

Now, divide both sides by 2.

$\frac{2x°}{2}=\frac{130°}{2}$

This will give us the value of x.

$x=65°$

Second side of the angle of the triangle is given as $x°$which is$65°$.

Third side of the angle of the triangle is given as$\left(x+25\right)°$.

Now add $65°$to it.

This gives us the value as,

$65{}^{\circ }+25{}^{\circ }=90°$

Step 4. Conclusion.

The value of x is$x=65°$.

Since one angle of the triangle is $90°$and the other two angles are $25°$and $65°$respectively.

Hence, it is a scalene right-angled triangle.