What is the measure of an angle formed by the angle bisector of a given angle and one of its sides: 171°30'

85.75° or 85°45'

You have 171°30' so you just cut it in half. 171°30' is the same as 171.5°. 171.5 divided by 2 is 85.75. There's your answer.

An angle bisector is one that cuts an angle into two equal halves.

bearing in mind that a degree has 60 minutes and a minute has 60 seconds, so then 171°30' is just 171 degrees and 30 minutes.

let's halve each, 171 : 2 = 85.5°, so 85.5° is really 85° and half of another degree, let's recall that a degree has 60 minutes, so half of a degree is just half of 60 minutes, namely 30 minutes, so 85.5° is really 85°30'.

let's halve the 30 minutes now, half of 30 is 15, so 15 minutes is its half.

now let's add both halves together, 85°30' plus 15', 85°45'.