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

Answer:

Angle CAB=56 degrees

Step-by-step 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,

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