Question

in the figure, m∠1=(x - 6)° and m∠2=(5x)°. (a) write an equation to find x. make sure you use an “=” sign in your answer. equation: (b) find the degree - measure of each angle. m∠1= m∠2=

Explanation:

Step1: Set up the equation

Since $\angle1$ and $\angle2$ are complementary (assuming they form a right - angle as they appear adjacent and the sum of adjacent angles forming a right - angle is 90 degrees), we have $(x - 6)+5x=90$.

Step2: Combine like terms

Combining the $x$ terms on the left - hand side gives $x+5x-6 = 90$, which simplifies to $6x-6 = 90$.

Step3: Add 6 to both sides

$6x-6 + 6=90 + 6$, so $6x=96$.

Step4: Solve for x

Dividing both sides by 6, we get $x=\frac{96}{6}=16$.

Step5: Find the measure of $\angle1$

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

Step6: Find the measure of $\angle2$

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

Answer:

(a) Equation: $(x - 6)+5x=90$
(b) $m\angle1 = 10^{\circ}$
$m\angle2 = 80^{\circ}$