Question

Can someone answer with steps and explanation? Thanks.

Answer 1

`x=-16\text{ or } x=7`

Explanation:

Since ΔABC is mapped onto ΔDEF, we can write that:

`\Delta ABC\cong \Delta DE F`

By CPCTC:

`\angle A\cong \angle D`

And since ΔABC is isosceles with Vertex C:

`\angle A \cong \angle B`

We are given that:

`m\angle D=34`

Hence:

`m\angle A=34=m\angle B`

We are also given that:

`m\angle C=x^2+9x`

The interior angles of a triangle must sum to 180°. Thus:

`m\angle A+m\angle B+m\angle C=180`

Substitute:

`(34)+(34)+(x^2+9x)=180`

Simplify:

`68+x^2+9x=180`

Isolate the equation:

`x^2+9x-112=0`

Factor:

`(x+16)(x-7)=0`

Zero Product Property:

`x+16=0\text{ or } x-7=0`

Solve for each case:

`x=-16\text{ or } x=7`

Testing the solutions, we can see that both yields C = 112°.

Hence, our solutions are:

`x=-16\text{ or } x=7`