Question

in the figure below, (mangle1 = 5x^{circ}) and (mangle2=(x - 24)^{circ}). find the angle measures.

Explanation:

Step1: Note angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (form a straight - line), $m\angle1 + m\angle2=180^{\circ}$.
So, $5x+(x - 24)=180$.

Step2: Simplify the equation

Combine like terms: $5x+x-24 = 180$, which gives $6x-24 = 180$.

Step3: Solve for $x$

Add 24 to both sides of the equation: $6x-24 + 24=180 + 24$, so $6x=204$.
Then divide both sides by 6: $x=\frac{204}{6}=34$.

Step4: Find $m\angle1$

Substitute $x = 34$ into the expression for $m\angle1$: $m\angle1=5x=5\times34 = 170^{\circ}$.

Step5: Find $m\angle2$

Substitute $x = 34$ into the expression for $m\angle2$: $m\angle2=x - 24=34-24 = 10^{\circ}$.

Answer:

$m\angle1 = 170^{\circ}$
$m\angle2 = 10^{\circ}$