Question

in the figure, (mangle1=(7x)^{circ}) and (mangle2=(x - 6)^{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.

Explanation:

Step1: Identify angle - relationship

From the figure, $\angle1$ and $\angle2$ are complementary. So, $m\angle1 + m\angle2=90^{\circ}$.

Step2: Substitute angle - measures

Substitute $m\angle1 = 7x$ and $m\angle2=x - 6$ into the equation: $7x+(x - 6)=90$.

Step3: Simplify the equation

Combine like - terms: $7x+x-6 = 90$, which simplifies to $8x-6 = 90$.
Add 6 to both sides: $8x=90 + 6$, so $8x=96$.
Divide both sides by 8: $x=\frac{96}{8}=12$.

Step4: Find $m\angle1$

Substitute $x = 12$ into $m\angle1 = 7x$. Then $m\angle1=7\times12 = 84^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 12$ into $m\angle2=x - 6$. Then $m\angle2=12-6 = 6^{\circ}$.

Answer:

(a) Equation: $7x+(x - 6)=90$
(b) $m\angle1 = 84^{\circ}$
$m\angle2 = 6^{\circ}$