Question

∠1 and ∠2 are supplementary angles. if (mangle1=(8x - 21)^{circ}) and (mangle2=(x - 24)^{circ}), then find the measure of ∠2.

Explanation:

Step1: Use supplementary - angle property

Since $\angle1$ and $\angle2$ are supplementary angles, $m\angle1 + m\angle2=180^{\circ}$. So, $(8x - 21)+(x - 24)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $8x+x-21 - 24 = 180$, which simplifies to $9x-45 = 180$.

Step3: Isolate the variable term

Add 45 to both sides of the equation: $9x-45 + 45=180 + 45$, resulting in $9x=225$.

Step4: Solve for $x$

Divide both sides by 9: $\frac{9x}{9}=\frac{225}{9}$, so $x = 25$.

Step5: Find the measure of $\angle2$

Substitute $x = 25$ into the expression for $m\angle2$. $m\angle2=(x - 24)^{\circ}=(25 - 24)^{\circ}=1^{\circ}$.

Answer:

$1^{\circ}$