Chapter 3, Problem 15RP

To determine

To calculate: The value of x

Answer to Problem 15RP

The value of x is ${11}^{\circ }$

Explanation of Solution

Given information: $\overline{AB}\cong \overline{AC}$ is provided in the question which will help to find the solution.

Formula used: Here, we are using middle term splitting.

Calculation: Here, $\angle B=\angle C$ (because opposite angles of equal sides are equal)

So, ${\left(x^2-6x\right)}^{\circ }={55}^{\circ }$

  $x^2-6x-55=0$

  $x^2-11x+5x-55=0$

  $x\left(x-11\right)+5(x-11)=0$

  $\left(x+5\right)\left(x-11\right)=0$

  $x=-5,x=11$

As, we cannot consider negative value.

Conclusion: Hence, the value of x is ${11}^{\circ }$