Question

in the figure, m∠1=(5x)° and m∠2=(x - 6)°. (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 can write the equation.
$5x+(x - 6)=180$

Step2: Simplify the left - hand side of the equation

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

Step3: Solve for x

Add 6 to both sides of the equation: $6x-6 + 6=180 + 6$, so $6x=186$. Then divide both sides by 6: $x=\frac{186}{6}=31$.

Step4: Find the measure of $\angle1$

Substitute $x = 31$ into the expression for $\angle1$: $m\angle1=5x=5\times31 = 155^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 31$ into the expression for $\angle2$: $m\angle2=x - 6=31-6 = 25^{\circ}$.

Answer:

(a) Equation: $5x+(x - 6)=180$
(b) $m\angle1 = 155^{\circ}$
$m\angle2 = 25^{\circ}$