Question

question
in $\triangle def$, $overline{df}$ is extended through point f to point g, $mangle fde = (x + 2)^circ$, $mangle def = (2x + 3)^circ$, and $mangle efg = (6x - 16)^circ$. what is the value of $x$?
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Apply exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So:
$$m\angle EFG = m\angle FDE + m\angle DEF$$

Step2: Substitute given angle expressions

Replace each angle with its algebraic form:
$$6x - 16 = (x + 2) + (2x + 3)$$

Step3: Simplify right-hand side

Combine like terms on the right:
$$6x - 16 = 3x + 5$$

Step4: Isolate x terms

Subtract $3x$ from both sides:
$$3x - 16 = 5$$

Step5: Solve for x

Add 16 to both sides, then divide by 3:
$$3x = 21 \implies x = \frac{21}{3} = 7$$

Answer:

$x=7$