Question

in the figure below, m∠1 = 2x° and m∠2=(x + 69)°. find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are supplementary (form a straight - line), $m\angle1 + m\angle2=180^{\circ}$. So, $2x+(x + 69)=180$.

Step2: Simplify the left - hand side

Combine like terms: $2x+x+69 = 3x+69$. So the equation becomes $3x+69 = 180$.

Step3: Solve for $x$

Subtract 69 from both sides: $3x=180 - 69=111$. Then divide both sides by 3: $x=\frac{111}{3}=37$.

Step4: Find $m\angle1$

Substitute $x = 37$ into the expression for $m\angle1$: $m\angle1=2x=2\times37 = 74^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 37$ into the expression for $m\angle2$: $m\angle2=x + 69=37+69 = 106^{\circ}$.

Answer:

$m\angle1 = 74^{\circ}$
$m\angle2 = 106^{\circ}$