Question

the angles are supplementary angles. determine the measures of ∠1 and ∠2. m∠1 = □°, and m∠2 = □°

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary, $m\angle1 + m\angle2=180^{\circ}$. Given $m\angle1 = 4x - 10$ and $m\angle2=x$, we have the equation $(4x - 10)+x = 180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side of the equation, we get $4x+x-10 = 180$, which simplifies to $5x-10 = 180$.

Step3: Add 10 to both sides

Adding 10 to both sides of the equation $5x-10 = 180$, we have $5x-10 + 10=180 + 10$, so $5x=190$.

Step4: Solve for x

Dividing both sides of the equation $5x = 190$ by 5, we get $x=\frac{190}{5}=38$.

Step5: Find the measure of $\angle1$

Substitute $x = 38$ into the expression for $m\angle1$: $m\angle1=4x-10=4\times38 - 10=152 - 10 = 142^{\circ}$.

Step6: Find the measure of $\angle2$

Since $m\angle2=x$, when $x = 38$, $m\angle2 = 38^{\circ}$.

Answer:

$m\angle1 = 142^{\circ}$, and $m\angle2 = 38^{\circ}$