Question

in $delta def$, $overline{df}$ is extended through point f to point g, $\text{m}angle fde = (x + 2)^circ$, $\text{m}angle def = (2x + 3)^circ$, and $\text{m}angle efg = (6x - 16)^circ$. what is the value of $x$?

Explanation:

Step1: Recall exterior angle theorem

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

Step2: Substitute given angle expressions

$$6x - 16 = (x + 2) + (2x + 3)$$

Step3: Simplify right-hand side

$$6x - 16 = 3x + 5$$

Step4: Isolate x terms

$$6x - 3x = 5 + 16$$

Step5: Calculate final value

$$3x = 21 \\ x = \frac{21}{3} = 7$$

Answer:

$7$