Question

in the figure below, m∠1 = 3x° and m∠2=(x + 22)°. find the angle measures.

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are complementary (the two - arrow lines form a right - angle), we know that $m\angle1 + m\angle2=90^{\circ}$.

Step2: Substitute angle measures

Substitute $m\angle1 = 3x^{\circ}$ and $m\angle2=(x + 22)^{\circ}$ into the equation $m\angle1 + m\angle2 = 90^{\circ}$. We get $3x+(x + 22)=90$.

Step3: Simplify the equation

Combine like terms: $3x+x+22 = 90$, which simplifies to $4x+22 = 90$.

Step4: Solve for x

Subtract 22 from both sides: $4x=90 - 22=68$. Then divide both sides by 4: $x=\frac{68}{4}=17$.

Step5: Find $m\angle1$ and $m\angle2$

For $m\angle1 = 3x^{\circ}$, substitute $x = 17$: $m\angle1=3\times17^{\circ}=51^{\circ}$.
For $m\angle2=(x + 22)^{\circ}$, substitute $x = 17$: $m\angle2=(17 + 22)^{\circ}=39^{\circ}$.

Answer:

$m\angle1 = 51^{\circ}$
$m\angle2 = 39^{\circ}$