Question

1. find x.

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $2x + 54=(x + 20)+3x$.

Step2: Simplify the equation

Expand the right - hand side: $2x+54=x + 20+3x$. Combine like terms: $2x+54 = 4x+20$.

Step3: Isolate the variable x

Subtract $2x$ from both sides: $54=4x - 2x+20$, which simplifies to $54 = 2x+20$. Then subtract 20 from both sides: $54 - 20=2x$, so $34 = 2x$.

Step4: Solve for x

Divide both sides by 2: $x=\frac{34}{2}=17$.

Answer:

$x = 17$