Question

two parallel lines are intersected by a transversal. ∠12 and ∠15 are consecutive exterior angles. the measure of ∠12 is (14a + 17)° and the measure of ∠15 is (26a + 43)°. what is the measure of each angle? enter the correct measure into the boxes. m∠12 = m∠15 =

Explanation:

Step1: Recall angle - relationship property

Consecutive exterior angles are supplementary when two parallel lines are intersected by a transversal. So, \(m\angle12 + m\angle15=180^{\circ}\).

Step2: Substitute angle - measures

Substitute \(m\angle12=(14a + 17)^{\circ}\) and \(m\angle15=(26a + 43)^{\circ}\) into the equation: \((14a + 17)+(26a + 43)=180\).

Step3: Simplify the left - hand side

Combine like terms: \(14a+26a+17 + 43=180\), which gives \(40a+60 = 180\).

Step4: Solve for \(a\)

Subtract 60 from both sides: \(40a=180 - 60=120\). Then divide both sides by 40: \(a=\frac{120}{40}=3\).

Step5: Find \(m\angle12\)

Substitute \(a = 3\) into the expression for \(m\angle12\): \(m\angle12=14\times3+17=42 + 17=59^{\circ}\).

Step6: Find \(m\angle15\)

Substitute \(a = 3\) into the expression for \(m\angle15\): \(m\angle15=26\times3+43=78 + 43=121^{\circ}\).

Answer:

\(m\angle12 = 59^{\circ}\)
\(m\angle15 = 121^{\circ}\)