Question

in the figure below, m∠1 = 5x° and m∠2=(x - 18)°. find the angle measures.
m∠1 =
m∠2 =

Explanation:

Step1: Set up equation

Since ∠1 and ∠2 are complementary (sum to 90°), we have $5x+(x - 10)=90$.

Step2: Simplify left - hand side

Combining like terms gives $6x-10 = 90$.

Step3: Solve for x

Add 10 to both sides: $6x=100$, then $x=\frac{100}{6}=\frac{50}{3}$.

Step4: Find angle measures

$m\angle1 = 5x=5\times\frac{50}{3}=\frac{250}{3}\approx83.33^{\circ}$, $m\angle2=x - 10=\frac{50}{3}-10=\frac{50 - 30}{3}=\frac{20}{3}\approx6.67^{\circ}$

Answer:

$m\angle1=\frac{250}{3}^{\circ}$, $m\angle2=\frac{20}{3}^{\circ}$