Radius be is a perpendicular bisector of chord ac. what is the measure of
a. 100°

b. 50°

c. 90°

d. 40°

A. 100°

Step-by-step explanation:

Let's take a look at the image and make some conclusions.

Angle BAE is 40 degrees

All angles at the crossing of BE and AC are right angles (90 degrees) because they are perpendicular lines.

Since BE is a bisector of angle ABC, we know that angles ABD and DBC are equal.

We don't know angle ABD but it's easy to find... since we know 2 angles from triangle ABE, and the sum of the interior triangles is 180.  So,

ABD = 180 - 40 - 90 = 50

Since ABD is 50 degrees and represents half of angle ABC... we know that ABC is 100 degrees.

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