What is x? mo is an angle bisector

 The correct option is (D) 24.

Step-by-step explanation:  We are given to find the value of x from the given figure, where MO is an angle bisector.

From the figure, we note that

MO is the angle bisector of angle M in ΔLMN, where

ML = x cm, MN = 12 cm, LO = 41 cm and ON = 7 cm.

We have the following theorem :

Angle bisector theorem : An angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.

Applying the above theorem in the given triangle LMN, we have

Thus, the required value of x is 24.

Option (D) is CORRECT.

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°

true

explanation: