Question

∠3 and ∠4 are supplementary angles. m∠3 = 6x + 1 and m∠4 = 2x + 19. draw a diagram, then solve to answer the following questions. x = m∠3 = (remember degrees!) m∠4 =

Explanation:

Step1: Use supplementary - angle property

Since $\angle3$ and $\angle4$ are supplementary angles, $m\angle3 + m\angle4=180^{\circ}$. So, $(6x + 1)+(2x + 19)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $6x+2x+1 + 19=180$, which simplifies to $8x+20 = 180$.

Step3: Isolate the variable term

Subtract 20 from both sides of the equation: $8x+20−20=180 - 20$, resulting in $8x=160$.

Step4: Solve for $x$

Divide both sides of the equation by 8: $\frac{8x}{8}=\frac{160}{8}$, so $x = 20$.

Step5: Find $m\angle3$

Substitute $x = 20$ into the expression for $m\angle3$: $m\angle3=6x + 1=6\times20+1=120 + 1=121^{\circ}$.

Step6: Find $m\angle4$

Substitute $x = 20$ into the expression for $m\angle4$: $m\angle4=2x + 19=2\times20+19=40 + 19=59^{\circ}$.

Answer:

$x = 20$
$m\angle3=121^{\circ}$
$m\angle4=59^{\circ}$