Question

in the figure, (mangle1=(6x)^{circ}) and (mangle2=(x + 13)^{circ}). (a) write an equation to find (x). make sure you sign in your answer. equation: (b) find the degree measure of each angle. (mangle1=) (^{circ}) (mangle2=) (^{circ})

Explanation:

Step1: Note angle - sum property

Since $\angle1$ and $\angle2$ are complementary, $m\angle1 + m\angle2=90^{\circ}$. So the equation is $6x+(x + 13)=90$.

Step2: Solve the equation for $x$

Combine like - terms: $7x+13 = 90$. Then $7x=90 - 13=77$, and $x = 11$.

Step3: Find angle measures

$m\angle1=6x=6\times11 = 66^{\circ}$, $m\angle2=x + 13=11+13 = 24^{\circ}$.

Answer:

(a) Equation: $6x+(x + 13)=90$
(b) $m\angle1 = 66^{\circ}$
$m\angle2 = 24^{\circ}$