Question

1. in the figure, m∠1=(x + 24)° and m∠2=(5x)°. (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 (a straight - line forms an angle of 180°), we have $(x + 24)+5x=180$.

Step2: Solve the equation for x

Combine like terms: $x+5x+24 = 180$, so $6x+24 = 180$. Subtract 24 from both sides: $6x=180 - 24=156$. Then divide both sides by 6: $x=\frac{156}{6}=26$.

Step3: Find the measure of $\angle1$

Substitute $x = 26$ into the expression for $\angle1$: $m\angle1=(x + 24)=(26+24)=50$.

Step4: Find the measure of $\angle2$

Substitute $x = 26$ into the expression for $\angle2$: $m\angle2 = 5x=5\times26 = 130$.

Answer:

(a) Equation: $(x + 24)+5x=180$
(b) $m\angle1 = 50$
$m\angle2 = 130$