Math Snap

STEP 1

1. Angles on a straight line are supplementary, meaning their measures add up to $180^\circ$.
2. $m \angle 1 = (8x)^\circ$ and $m \angle 2 = (x-9)^\circ$.

STEP 2

1. Write the equation for $x$.
2. Solve for $x$.
3. Calculate the measure of each angle.

STEP 3

Since angles on a straight line are supplementary, we have:
$$m \angle 1 + m \angle 2 = 180^\circ$$ Substitute the given expressions:
$$(8x) + (x - 9) = 180$$

STEP 4

Combine like terms in the equation:
$$8x + x - 9 = 180$$ $$9x - 9 = 180$$

STEP 5

Add $9$ to both sides to isolate the term with $x$:
$$9x - 9 + 9 = 180 + 9$$ $$9x = 189$$

STEP 6

Divide both sides by $9$ to solve for $x$:
$$x = \frac{189}{9}$$ $$x = 21$$

STEP 7

Substitute $x = 21$ back into the expressions for each angle:
$$m \angle 1 = (8 \times 21)^\circ$$ $$m \angle 1 = 168^\circ$$

Calculate $m \angle 2$:
$$m \angle 2 = (21 - 9)^\circ$$ $$m \angle 2 = 12^\circ$$ The equation to find $x$ is:
Ecuación: $8x + (x - 9) = 180$
The measures of the angles are:
$$\begin{array}{l} m \angle 1 = 168^\circ \\ m \angle 2 = 12^\circ \end{array}$$