Question

in the figure, (mangle1=(x - 6)^{circ}) and (mangle2=(5x)^{circ}). (a) write an equation to find (x). make sure you use an \=\ sign in your answer. (b) find the degree measure of each angle. (mangle1=square^{circ}) (mangle2=square^{circ})

Explanation:

Step1: Identify angle relationship

Since $\angle1$ and $\angle2$ are complementary (they form a right - angle), we have the equation $m\angle1 + m\angle2=90^{\circ}$.
$(x - 6)+5x=90$

Step2: Solve the equation for $x$

Combine like terms:
$x-6 + 5x=90$
$6x-6=90$
Add 6 to both sides:
$6x=90 + 6$
$6x=96$
Divide both sides by 6:
$x=\frac{96}{6}=16$

Step3: Find $m\angle1$

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

Step4: Find $m\angle2$

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

Answer:

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