Question

In Circle M, points A, B, and C are located on the circle such that measure angle CBM equals to 34 degrees. What represents angle CAB

Answer 1

The answer is Angle CAB=56 degrees

Explanation:

Answer 2

Angle CAB=56 degrees

Explanation:

See the attached image for the diagram.

In triangle BMC

|BM|=|MC| (Radii of a Circle)

Therefore, triangle BMC is an Isosceles Triangle; and

`\angle CBM=\angle BCM=34^\circ`

`\angle CBM+\angle BCM+\angle BMC=180^\circ$ (sum of \angle s$ in a triangle)\\34^\circ+34^\circ+\angle BMC=180^\circ\\\angle BMC=180^\circ-68^\circ=112^\circ`

Next,

`\angle BMC=2\angle CAB $(Angle at center is twice angle at circumference)\\112^\circ=2\angle CAB\\\angle CAB=112^\circ / 2\\\angle CAB=56^\circ`