Question

in the figure below, (mangle1 = 6x^{circ}) and (mangle2=(x + 6)^{circ}). find the angle measures.

Explanation:

Step1: Set up equation

Since $\angle1$ and $\angle2$ are complementary (sum to 90° as they form a right - angle), we have the equation $6x+(x + 6)=90$.

Step2: Simplify left - hand side

Combine like terms: $6x+x+6=90$, which gives $7x+6 = 90$.

Step3: Isolate the variable term

Subtract 6 from both sides: $7x=90 - 6$, so $7x=84$.

Step4: Solve for x

Divide both sides by 7: $x=\frac{84}{7}=12$.

Step5: Find measure of $\angle1$

Substitute $x = 12$ into the expression for $m\angle1$: $m\angle1=6x=6\times12 = 72^{\circ}$.

Step6: Find measure of $\angle2$

Substitute $x = 12$ into the expression for $m\angle2$: $m\angle2=x + 6=12+6=18^{\circ}$.

Answer:

$m\angle1 = 72^{\circ}$
$m\angle2 = 18^{\circ}$