Question

The measure of MKJ is 80°. After analyzing the diagram, Janelle concludes that is an angle bisector.

Answer 1

Answer:

Janelle's conclusion is correct, because the value of x is 15

Step-by-step explanation:

step 1

Find the value of x

we know that

m∠MKJ=m∠LKM+m∠LKJ

substitute the given values and solve for x

80°=(2x+10)°+(3x-5)°

80=5x+5

5x=80-5

5x=75

x=15

step 2

Find the value of x assuming that KL bisect the angle MKJ

so

m∠LKM=m∠LKJ

(2x+10)°=(3x-5)°

3x-2x=10+5

x=15

therefore

Janelle's conclusion is correct, because the value of x is 15

Answer 2

Answer:

Option c

Step-by-step explanation:

Measure of angle MKJ = 80°

Since KL is the bisector of ∠MKJ

Therefore, [m∠(MKJ) = m∠(MKL) + m∠(LKJ)]

80° = m∠(MKL) + m∠(LKJ)

∠MKL = (2x+10)° and ∠(LKJ) = (3x-5)°     [given in the figure]

Therefore, (2x-10) + (3x-5) = 80

                 5x + 5 = 80

                 5x = 80 - 5

                 5x = 75

                 x = $\frac{75}{5}$

                 x = 15

That means for x = 15 line segment KL is the bisector of ∠MKJ.

Option C will be the answer.