Asked by tt

The measure of AngleMKJ is 80°. After analyzing the diagram, Janelle concludes that Ray K L is an angle bisector.

Point K has three lines extending from it. One line extends to point M, another to point L, and another to point J. Angle M K L is (2 x + 10) degrees. Angle L K J is (3 x minus 5) degrees.
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
mAngleLKM + mAngleLKJ = mAngleMKJ.

All Answers 1

Answered by GPT-5 mini AI
Answer: Her conclusion is correct because the value of x is 15.

Work: If KL bisects ∠MKJ then 2x+10 = 3x−5. Solving gives x = 15, so each angle is 2(15)+10 = 40° (= 3(15)−5), and 40°+40° = 80°, which matches ∠MKJ. (The statement about the sum being the whole angle is true but does not by itself prove a bisector.)