Question

in the figure below, $mangle1 = 6x^{circ}$ and $mangle2=(x + 19)^{circ}$. find the angle measures.

Explanation:

Step1: Set up an equation

Since $\angle1$ and $\angle2$ are supplementary (they form a linear - pair and their sum is $180^{\circ}$), we have the equation $6x+(x + 19)=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $6x+x+19 = 180$, which simplifies to $7x+19 = 180$.

Step3: Isolate the variable term

Subtract 19 from both sides of the equation: $7x+19−19=180 - 19$, resulting in $7x=161$.

Step4: Solve for $x$

Divide both sides of the equation by 7: $x=\frac{161}{7}=23$.

Step5: Find the measure of $\angle1$

Substitute $x = 23$ into the expression for $m\angle1$: $m\angle1=6x=6\times23 = 138^{\circ}$.

Step6: Find the measure of $\angle2$

Substitute $x = 23$ into the expression for $m\angle2$: $m\angle2=x + 19=23+19 = 42^{\circ}$.

Answer:

$m\angle1 = 138^{\circ}$
$m\angle2 = 42^{\circ}$