Question

in the figure below, m∠1=(x - 6)° and m∠2 = 7x°. find the angle measures.

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are complementary (the angle formed is a right - angle, $90^{\circ}$), we have $m\angle1 + m\angle2=90^{\circ}$.
$(x - 6)+7x=90$

Step2: Combine like terms

Combine the $x$ terms on the left - hand side:
$x+7x-6 = 90$
$8x-6 = 90$

Step3: Isolate the variable term

Add 6 to both sides of the equation:
$8x-6 + 6=90 + 6$
$8x=96$

Step4: Solve for $x$

Divide both sides by 8:
$x=\frac{96}{8}=12$

Step5: Find $m\angle1$

Substitute $x = 12$ into the expression for $m\angle1$:
$m\angle1=(x - 6)^{\circ}=(12 - 6)^{\circ}=6^{\circ}$

Step6: Find $m\angle2$

Substitute $x = 12$ into the expression for $m\angle2$:
$m\angle2=7x^{\circ}=7\times12^{\circ}=84^{\circ}$

Answer:

$m\angle1 = 6^{\circ}$
$m\angle2 = 84^{\circ}$