Question

1. ∠1 and ∠2 are supplementary and m∠1 = 8x - 23 and m∠2 = 6x + 35. what is the m∠1 and m∠2?

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$. So, $(8x - 23)+(6x + 35)=180$.

Step2: Combine like - terms

$8x+6x-23 + 35=180$, which simplifies to $14x+12 = 180$.

Step3: Solve for $x$

Subtract 12 from both sides: $14x=180 - 12=168$. Then divide both sides by 14, $x=\frac{168}{14}=12$.

Step4: Find $m\angle1$

Substitute $x = 12$ into the expression for $m\angle1$: $m\angle1=8x-23=8\times12-23=96 - 23=73^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 12$ into the expression for $m\angle2$: $m\angle2=6x + 35=6\times12+35=72 + 35=107^{\circ}$.

Answer:

$m\angle1 = 73^{\circ}$, $m\angle2=107^{\circ}$