Question

in the figure, m∠1=(6x)° and m∠2=(x - 8)°. (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: Identify angle - relationship

Since the two angles are complementary (as they form a right - angle), their sum is 90 degrees. So, the equation is $6x+(x - 8)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $6x+x-8 = 90$, which simplifies to $7x-8 = 90$.

Step3: Isolate the variable term

Add 8 to both sides of the equation: $7x-8 + 8=90 + 8$, resulting in $7x=98$.

Step4: Solve for x

Divide both sides by 7: $\frac{7x}{7}=\frac{98}{7}$, so $x = 14$.

Step5: Find the measure of angle 1

Substitute $x = 14$ into the expression for $m\angle1$: $m\angle1=6x=6\times14 = 84^{\circ}$.

Step6: Find the measure of angle 2

Substitute $x = 14$ into the expression for $m\angle2$: $m\angle2=x - 8=14-8 = 6^{\circ}$.

Answer:

(a) Equation: $6x+(x - 8)=90$
(b) $m\angle1 = 84^{\circ}$
$m\angle2 = 6^{\circ}$