Question

Given triangle CAT is congruent to triangle DOG. Solve for x

Answer 1

The value of x is 2 or -5.5.

Step-by-step explanation:

Given that triangle CAT is congruent to triangle DOG, then we have that:

`\angle T\cong\angle G`

Step 1: We determine the value of angle T.

`\begin{gathered} \angle T=180^0-(87^0+75^0) \\ =180^0-162^0 \\ =18^0 \end{gathered}`

Step 2: Since angle T is congruent to angle G, then:

`(x+4)(2x-1)=18`

Step 3: We solve the equation above for x.

`\begin{gathered} 2x^2-x+8x-4-18=0 \\ 2x^2+7x-22=0 \\ 2x^2-4x+11x-22=0 \\ 2x(x-2)+11(x-2)=0 \\ (2x+11)(x-2)=0 \end{gathered}`

Therefore:

`\begin{gathered} 2x+11=0\text{ or x-2=0} \\ 2x=-11\text{ or x=2} \\ x=-5.5\text{ or x=2} \end{gathered}`

The value of x is 2 or -5.5.