Question

in the figure, m∠1=(x + 12)° 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 $\angle2$ form a linear - pair, their sum is 180 degrees. So the equation is $(x + 12)+5x=180$.

Step2: Simplify the equation

Combine like terms: $x+12 + 5x=180$ becomes $6x+12 = 180$.

Step3: Solve for x

Subtract 12 from both sides: $6x=180 - 12=168$. Then divide both sides by 6: $x=\frac{168}{6}=28$.

Step4: Find the measure of $\angle1$

Substitute $x = 28$ into the expression for $\angle1$: $m\angle1=(x + 12)=(28+12)=40^{\circ}$.

Step5: Find the measure of $\angle2$

Substitute $x = 28$ into the expression for $\angle2$: $m\angle2=(5x)=5\times28 = 140^{\circ}$.

Answer:

(a) Equation: $(x + 12)+5x=180$
(b) $m\angle1 = 40^{\circ}$
$m\angle2 = 140^{\circ}$