Question

two parallel lines are intersected by a transversal. ∠3 and ∠9 are alternate interior angles. the measure of ∠3 is (4m + 1)°. the measure of ∠9 is (187 - 2m)°. what is the measure of each angle? enter the correct measure in the boxes. m∠3 = m∠9 =

Explanation:

Step1: Use property of alternate - interior angles

Since alternate - interior angles formed by two parallel lines intersected by a transversal are congruent, we set up the equation $4m + 1=187−2m$.

Step2: Solve the equation for $m$

Add $2m$ to both sides: $4m+2m + 1=187−2m+2m$, which simplifies to $6m + 1=187$. Then subtract 1 from both sides: $6m+1 - 1=187 - 1$, getting $6m=186$. Divide both sides by 6: $m=\frac{186}{6}=31$.

Step3: Find the measure of $\angle3$

Substitute $m = 31$ into the expression for $\angle3$: $m\angle3=4m + 1=4\times31+1=124 + 1=125^{\circ}$.

Step4: Find the measure of $\angle9$

Substitute $m = 31$ into the expression for $\angle9$: $m\angle9=187−2m=187-2\times31=187 - 62=125^{\circ}$.

Answer:

$m\angle3 = 125^{\circ}$
$m\angle9 = 125^{\circ}$