Question

in the figure below, m∠1 = 3x° and m∠2=(x + 72)°. find the angle measures.

Explanation:

Step1: Set up equation based on linear - pair

Since $\angle1$ and $\angle2$ form a linear - pair, their sum is $180^{\circ}$. So, $3x+(x + 72)=180$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $3x+x+72 = 180$, which simplifies to $4x+72 = 180$.

Step3: Isolate the variable term

Subtract 72 from both sides: $4x+72−72=180 - 72$, resulting in $4x=108$.

Step4: Solve for $x$

Divide both sides by 4: $\frac{4x}{4}=\frac{108}{4}$, so $x = 27$.

Step5: Find the measure of $\angle1$

Substitute $x = 27$ into the expression for $\angle1$: $m\angle1=3x=3\times27 = 81^{\circ}$.

Step6: Find the measure of $\angle2$

Substitute $x = 27$ into the expression for $\angle2$: $m\angle2=x + 72=27+72 = 99^{\circ}$.

Answer:

$m\angle1 = 81^{\circ}$
$m\angle2 = 99^{\circ}$