Question

In triangle ABC, the perpendicular bisector of side AB intersects the extension of side AC at point D. Find the measure of angle ABC if angle CBD is 16 degrees and angle ACB is 118 degrees.

Answer 1

To find angle ABC, we utilize the sum of angles in a triangle and the properties of a perpendicular bisector. Angle ABC is calculated to be 46 degrees.

Step-by-step explanation:

To find the measure of angle ABC in the given triangle, we first note that the perpendicular bisector of AB means that angle ABD is also 16 degrees because it will form two congruent triangles ADB and BDC being isosceles. Since angles CBD and ABD are equal, and we know angle ACB measures 118 degrees, we can use the fact that the sum of angles in a triangle is 180 degrees to find the missing angle.

So, we calculate angle ABC by subtracting the sum of angles CBD and ACB from 180 degrees. This gives us:

Angle ABC = 180 - Angle CBD - Angle ACB

Angle ABC = 180 - 16 - 118

Angle ABC = 180 - 134

Angle ABC = 46 degrees.

Thus, the measure of angle ABC is 46 degrees.