Question

in the figure, ( mangle 1=(5x)^circ ) and ( mangle 2=(x - 6)^circ ).
(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.
( mangle 1=square^circ )
( mangle 2=square^circ )

Explanation:

Step1: Identify angle relationship

The figure shows $\angle 1$ and $\angle 2$ form a right angle ($90^\circ$), so their sum equals $90^\circ$.
$5x + (x - 6) = 90$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$.

$$\begin{align*} 5x + x - 6 &= 90\\ 6x - 6 &= 90\\ 6x &= 96\\ x &= \frac{96}{6} = 16 \end{align*}$$

Step3: Calculate $m\angle1$

Substitute $x=16$ into $m\angle1=5x$.
$m\angle1 = 5\times16 = 80$

Step4: Calculate $m\angle2$

Substitute $x=16$ into $m\angle2=x-6$.
$m\angle2 = 16 - 6 = 10$

Answer:

(a) Equation: $5x + (x - 6) = 90$
(b)
$m\angle 1 = 80^\circ$
$m\angle 2 = 10^\circ$