Chapter 10.1, Problem 4E

To determine

To find the value of x and classify the triangle

Answer to Problem 4E

The value of $x={65}^{\circ }$

The triangle is a Scalene right-angled triangle

Explanation of Solution

Given information:

One angle of the triangle is ${25}^{\circ }$

Second angle of the triangle is $x^{\circ }$

Third angle of the triangle is ${\left(x+25\right)}^{\circ }$

Calculation:

The sum of all the angles of a triangle is ${180}^{\circ }$

This gives us-

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

Add both x and both numbers together

  $2x+{50}^{\circ }={180}^{\circ }$

Subtract 50 from both the sides

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

This gives us −

  $2x={130}^{\circ }$

Now, divide both sides by 2

  $\frac{2x^{\circ }}{2}=\frac{{130}^{\circ }}{2}$

This will give us the value of x

  $x={65}^{\circ }$

Second side of the angle of the triangle is given as $x^{\circ }$ which is ${65}^{\circ }$

Third side of the angle of the triangle is given as ${\left(x+25\right)}^{\circ }$

Now add ${65}^{\circ }$ to it.

This gives us the value as

  ${65}^{\circ }+{25}^{\circ }={90}^{\circ }$

Conclusion- The value of $x={65}^{\circ }$

Since one angle of the triangle is ${90}^{\circ }$ and the other two angles are ${25}^{\circ }$ and ${65}^{\circ }$ respectively.

Hence, it is aScalene right-angledtriangle