Question

in the figure below, m∠1=(x - 6)° and m∠2 = 5x°. find the angle measures.

Explanation:

Step1: Identify angle relationship

Since $\angle1$ and $\angle2$ are complementary (form a right - angle), $m\angle1 + m\angle2=90^{\circ}$.

Step2: Substitute angle expressions

Substitute $m\angle1=(x - 6)^{\circ}$ and $m\angle2 = 5x^{\circ}$ into the equation: $(x - 6)+5x=90$.

Step3: Combine like terms

Combine the $x$ terms: $x+5x-6 = 90$, which simplifies to $6x-6=90$.

Step4: Solve for $x$

Add 6 to both sides: $6x=90 + 6=96$. Then divide both sides by 6: $x=\frac{96}{6}=16$.

Step5: Find $m\angle1$

Substitute $x = 16$ into the expression for $m\angle1$: $m\angle1=(16 - 6)^{\circ}=10^{\circ}$.

Step6: Find $m\angle2$

Substitute $x = 16$ into the expression for $m\angle2$: $m\angle2=5\times16^{\circ}=80^{\circ}$.

Answer:

$m\angle1 = 10^{\circ}$
$m\angle2 = 80^{\circ}$