Question

1. ∠3 and ∠4 are supplementary angles. find the measures of the angles when m∠3=(6x + 59)° and m∠4=(3x - 14)°. m∠3 = m∠4 =

Explanation:

Step1: Use supplementary - angle property

Since $\angle3$ and $\angle4$ are supplementary, $m\angle3 + m\angle4=180^{\circ}$. So, $(6x + 59)+(3x - 14)=180$.

Step2: Simplify the left - hand side

Combine like terms: $6x+3x+59 - 14=180$, which gives $9x + 45=180$.

Step3: Solve for $x$

Subtract 45 from both sides: $9x=180 - 45$, so $9x = 135$. Then divide both sides by 9: $x=\frac{135}{9}=15$.

Step4: Find $m\angle3$

Substitute $x = 15$ into the expression for $m\angle3$: $m\angle3=6x + 59=6\times15+59=90 + 59 = 149^{\circ}$.

Step5: Find $m\angle4$

Substitute $x = 15$ into the expression for $m\angle4$: $m\angle4=3x - 14=3\times15-14=45 - 14 = 31^{\circ}$.

Answer:

$m\angle3 = 149^{\circ}$, $m\angle4 = 31^{\circ}$