Question

in the figure, m∠1=(5x)° and m∠2=(x - 24)°. (a) write an equation to find x. make sure you use an = sign in your answer. equation: (b) find the degree measure of each angle. m∠1 = m∠2 =

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (linear - pair of angles), the sum of their measures is $180^{\circ}$. So the equation is $5x+(x - 24)=180$.

Step2: Simplify the left - hand side of the equation

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

Step3: Isolate the variable term

Add 24 to both sides of the equation: $6x-24 + 24=180 + 24$, resulting in $6x=204$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{204}{6}=34$.

Step5: Find the measure of $\angle1$

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

Step6: Find the measure of $\angle2$

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

Answer:

(a) Equation: $5x+(x - 24)=180$
(b) $m\angle1 = 170^{\circ}$, $m\angle2 = 10^{\circ}$