Question

the angles are supplementary angles. determine the measures of ∠1 and ∠2.

m∠1 = □°, and m∠2 = □°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, if $\angle1 = 2x - 1$ and $\angle2=x$, then $(2x - 1)+x=180$.

Step2: Combine like - terms

$2x+x - 1=180$, which simplifies to $3x-1 = 180$.

Step3: Add 1 to both sides

$3x-1 + 1=180 + 1$, so $3x=181$.

Step4: Solve for x

$x=\frac{181}{3}\approx60.33$.

Step5: Find measure of $\angle1$

$\angle1=2x - 1=2\times\frac{181}{3}-1=\frac{362}{3}-1=\frac{362 - 3}{3}=\frac{359}{3}\approx119.67$.

Step6: Find measure of $\angle2$

$\angle2=x=\frac{181}{3}\approx60.33$.

Answer:

$m\angle1=\frac{359}{3}\approx119.67$; $m\angle2=\frac{181}{3}\approx60.33$