Question

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

Explanation:

Step1: Identify angle - relationship

Since the two angles are complementary (sum to 90° as they form a right - angle), we have the equation $5x+(x - 6)=90$.

Step2: Simplify the equation

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

Step3: Solve for x

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

Step4: Find the measure of ∠1

Substitute $x = 16$ into the expression for $m\angle1$: $m\angle1=5x=5\times16 = 80^{\circ}$.

Step5: Find the measure of ∠2

Substitute $x = 16$ into the expression for $m\angle2$: $m\angle2=x - 6=16-6 = 10^{\circ}$.

Answer:

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