Question

In the figure below, triangles BCN and NMB are right triangles, with right angles C and M, and segment MN is an angle-bisector. If m CNB = 60 degrees, which is m CBM?

Answer 30 degrees
45 degrees
60 degrees
75 degrees
.

Answer 1

r u shure

Answer 2

Angle BCN =90
Angle NMB=90
Angle CNB =60
Also given that MN is an angle-bisector (bisecting the angle CNB into two equal parts
MNC =MNB =30) refer to the attached figure

In a triangle sum of three angle should be 180.
angle BCN +angle CNB + angle CBN =180
This gives us angle CBN =180-90-60=30

Now, In the right triangle NMB,
angle NMB + angle MNB + angle NBM =180
angle NBM=180-90-30 (as angle MNB =30 from bisection )
=60

From the figure
Angle NBM= angle CBM+angle CBN
angle CBM=Angle NBM-angle CBN = 60-30 =30
So, angle CBM=30 degrees