Question

in the figure below, m∠1=(x + 81)° and m∠2 = 2x°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), $m\angle1 + m\angle2=180^{\circ}$. So, $(x + 81)+2x=180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side, we get $3x+81 = 180$.

Step3: Isolate the variable term

Subtract 81 from both sides: $3x=180 - 81$, so $3x=99$.

Step4: Solve for $x$

Divide both sides by 3: $x=\frac{99}{3}=33$.

Step5: Find $m\angle1$

Substitute $x = 33$ into the expression for $m\angle1$: $m\angle1=x + 81=33+81 = 114^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 33$ into the expression for $m\angle2$: $m\angle2=2x=2\times33 = 66^{\circ}$.

Answer:

$m\angle1 = 114^{\circ}$
$m\angle2 = 66^{\circ}$