Question

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

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (they form a right - angle, so $m\angle1 + m\angle2=90^{\circ}$), we have the equation $(x + 42)+2x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $3x+42 = 90$.

Step3: Isolate the variable term

Subtract 42 from both sides: $3x=90 - 42$, so $3x=48$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{48}{3}=16$.

Step5: Find $m\angle1$

Substitute $x = 16$ into the expression for $m\angle1$: $m\angle1=(x + 42)^{\circ}=(16 + 42)^{\circ}=58^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 16$ into the expression for $m\angle2$: $m\angle2=2x^{\circ}=2\times16^{\circ}=32^{\circ}$.

Answer:

$m\angle1 = 58^{\circ}$
$m\angle2 = 32^{\circ}$