Question

in the figure, m∠1=(5x)° and m∠2=(x - 11)°. (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 is 180°), we can write the equation $m\angle1 + m\angle2=180$.
$5x+(x - 11)=180$

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+x-11 = 180$, which simplifies to $6x-11 = 180$.

Step3: Solve for x

Add 11 to both sides: $6x-11 + 11=180 + 11$, so $6x=191$. Then divide both sides by 6: $x=\frac{191}{6}$.

Step4: Find the measure of $\angle1$

Substitute $x=\frac{191}{6}$ into the expression for $m\angle1$: $m\angle1 = 5x=5\times\frac{191}{6}=\frac{955}{6}\approx159.17^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = \frac{191}{6}$ into the expression for $m\angle2$: $m\angle2=x - 11=\frac{191}{6}-11=\frac{191-66}{6}=\frac{125}{6}\approx20.83^{\circ}$.

Answer:

(a) Equation: $5x+(x - 11)=180$
(b) $m\angle1=\frac{955}{6}^{\circ}$
$m\angle2=\frac{125}{6}^{\circ}$