Question

if ( m angle efh = (5x + 1)^circ ), ( m angle hfg = 62^circ ), and ( m angle efg = (18x + 11)^circ ), find ( x ) (accompanied by a diagram showing points ( e ), ( h ), ( g ) emanating from point ( f ))

Explanation:

Step1: Identify angle addition postulate

The measure of $\angle EFG$ is the sum of $\angle EFH$ and $\angle HFG$. So, $m\angle EFG = m\angle EFH + m\angle HFG$.

Step2: Substitute given values

Substitute $m\angle EFH = (5x + 1)^\circ$, $m\angle HFG = 62^\circ$, and $m\angle EFG = (18x + 11)^\circ$ into the equation:
$$18x + 11 = (5x + 1) + 62$$

Step3: Simplify the right - hand side

Simplify $(5x + 1)+62$:
$$18x + 11 = 5x+63$$

Step4: Subtract $5x$ from both sides

Subtract $5x$ from each side of the equation:
$$18x - 5x+11=5x - 5x + 63$$
$$13x+11 = 63$$

Step5: Subtract 11 from both sides

Subtract 11 from both sides:
$$13x+11 - 11=63 - 11$$
$$13x=52$$

Step6: Divide both sides by 13

Divide both sides by 13:
$$x=\frac{52}{13}$$
$$x = 4$$

Answer:

$x = 4$