Chapter 10.1, Problem 10E

To determine

To find the value of x and classify the triangle

Answer to Problem 10E

The value of $x={49}^{\circ }$

The triangle is a scalene right-angled triangle

Explanation of Solution

Given information:

One angle of the triangle is given as ${49}^{\circ }$

Second angle is given as ${41}^{\circ }$

Third angle is given as ${\left(2x-8\right)}^{\circ }$

Calculation:

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

This gives us-

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

Add both numbers together will give us

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

Subtract 90 from both the sides

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

This gives us −

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

Now, add both sides with 8

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

This gives us-

  $2x^{\circ }={98}^{\circ }$

Now, divide both sides by 2

  ${\frac{2x}{2}}^{\circ }=\frac{{98}^{\circ }}{2}$

This will give us-

  $x={49}^{\circ }$

Since, the thirdangleof the triangle is given as ${\left(2x-8\right)}^{\circ }$

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

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

So, the third angle is ${90}^{\circ }$

Conclusion- The value of $x={49}^{\circ }$ and the angle measurement is ${90}^{\circ }$

One angle is ${49}^{\circ }$ , Second angle is ${41}^{\circ }$ and the third angle is ${90}^{\circ }$

Since, all the three angles of the triangle are different and one of them is ${90}^{\circ }$

Hence, it is scalene right-angledtriangle