Question

the measure of ∠mkj is 80°. after analyzing the diagram, janelle concludes that (overrightarrow{kl}) is an angle bisector. which statement best describes janelles conclusion? her conclusion is incorrect because (2x + 10) is not equal to (3x - 5). her conclusion is incorrect because the angles are not marked; therefore, no conclusion can be drawn. her conclusion is correct because the value of (x) is 15. her conclusion is correct because (m∠lkm + m∠lkj = m∠mkj).

Explanation:

Step1: Recall the definition of an angle bisector

An angle bisector divides an angle into two equal - measure angles. If \(KL\) is an angle bisector of \(\angle MKJ\), then \(m\angle LKM=m\angle LKJ\). So, \(2x + 10=3x−5\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation \(2x + 10=3x−5\).
\(2x-2x + 10=3x-2x−5\), which simplifies to \(10=x - 5\).
Add 5 to both sides: \(x=10 + 5=15\).

Step3: Check the sum of angles

If \(x = 15\), then \(m\angle LKM=2x+10=2\times15 + 10=40^{\circ}\) and \(m\angle LKJ=3x−5=3\times15−5 = 40^{\circ}\), and \(m\angle LKM+m\angle LKJ=40^{\circ}+40^{\circ}=80^{\circ}=m\angle MKJ\)

Answer:

Her conclusion is correct because \(m\angle LKM + m\angle LKJ=m\angle MKJ\)