Question

in the figure below, m∠1 = 5x° and m∠2=(x + 42)°. find the angle measures.

Explanation:

Step1: Set up an equation

Since $\angle1$ and $\angle2$ are supplementary (they form a straight - line), $m\angle1 + m\angle2=180^{\circ}$. So, $5x+(x + 42)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+x+42=180$, which gives $6x + 42=180$.

Step3: Isolate the variable term

Subtract 42 from both sides: $6x=180 - 42$, so $6x=138$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{138}{6}=23$.

Step5: Find the measure of $\angle1$

Substitute $x = 23$ into the expression for $m\angle1$: $m\angle1=5x=5\times23 = 115^{\circ}$.

Step6: Find the measure of $\angle2$

Substitute $x = 23$ into the expression for $m\angle2$: $m\angle2=x + 42=23+42=65^{\circ}$.

Answer:

$m\angle1 = 115^{\circ}$
$m\angle2 = 65^{\circ}$