Question

in the figure below, m∠1=(x + 18)° and m∠2 = 3x°. find the angle measures.

Explanation:

Step1: Note angle - relationship

Since $\angle1$ and $\angle2$ are complementary (the angle formed by the two - ray intersection is a right - angle, so $\angle1+\angle2 = 90^{\circ}$), we have the equation $(x + 18)+3x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side of the equation, we get $x+3x + 18=90$, which simplifies to $4x+18 = 90$.

Step3: Isolate the variable term

Subtract 18 from both sides of the equation: $4x+18−18=90 - 18$, so $4x=72$.

Step4: Solve for $x$

Divide both sides of the equation by 4: $\frac{4x}{4}=\frac{72}{4}$, so $x = 18$.

Step5: Find $m\angle1$

Substitute $x = 18$ into the expression for $m\angle1$: $m\angle1=(x + 18)^{\circ}=(18 + 18)^{\circ}=36^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 18$ into the expression for $m\angle2$: $m\angle2=3x^{\circ}=3\times18^{\circ}=54^{\circ}$.

Answer:

$m\angle1 = 36^{\circ}$
$m\angle2 = 54^{\circ}$