Question

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

Which statement best describes Janelle's 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
mLKM + mLKJ = mMKJ.

Answer 1

Option c

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 =
`(75)/(5)`

x = 15

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

Option C will be the answer.

Answer 2

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

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