Question

in the figure below, m∠1=(x - 4)° and m∠2 = 7x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (a straight - line angle is 180°), we have $(x - 4)+7x=180$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $x+7x-4 = 180$, which simplifies to $8x-4 = 180$.

Step3: Add 4 to both sides

Adding 4 to both sides of the equation: $8x-4 + 4=180 + 4$, resulting in $8x=184$.

Step4: Solve for x

Dividing both sides by 8: $x=\frac{184}{8}=23$.

Step5: Find $m\angle1$

Substitute $x = 23$ into the expression for $m\angle1$: $m\angle1=(x - 4)=(23 - 4)=19^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 23$ into the expression for $m\angle2$: $m\angle2=7x=7\times23 = 161^{\circ}$.

Answer:

$m\angle1 = 19^{\circ}$
$m\angle2 = 161^{\circ}$