Question

1. find the value of x.

(4x + 7)°
(17x + 13)°
97°
22.5
21.125
9.28
7

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle $XWY$, the exterior angle at $Y$ is $(17x + 13)^{\circ}$, and the two non - adjacent interior angles are $(4x + 7)^{\circ}$ and $97^{\circ}$. So, we can set up the equation $17x+13=(4x + 7)+97$.

Step2: Simplify the right - hand side of the equation

$(4x + 7)+97=4x+(7 + 97)=4x + 104$. So the equation becomes $17x+13 = 4x+104$.

Step3: Isolate the variable terms

Subtract $4x$ from both sides: $17x-4x+13=4x-4x + 104$, which simplifies to $13x+13 = 104$.

Step4: Isolate the variable $x$

Subtract 13 from both sides: $13x+13 - 13=104 - 13$, getting $13x=91$.

Step5: Solve for $x$

Divide both sides by 13: $x=\frac{91}{13}=7$.

Answer:

$7$