Question

By constructing an angle bisector for each of the following angles, find out the measure of the angles that will be formed after the construction.
a) 50° b) 74° c) 105° [3 Marks]

Answer 1

When an angle bisector is constructed for an angle of the measure, say X, then, it is divided into two equal halves, which means, two angles of measure X/2 are formed.

a) Let X = 50°. The angle bisector makes two angles of measure $\frac{X}{2}$, which is 25° each. [1 mark]
b) Let X = 74°. The angle bisector makes two angles of measure $\frac{X}{2}$, which is 37° each. [1 mark]
c) Let X = 105°. The angle bisector makes two angles of measure $\frac{X}{2}$, which is 52.5° each. [1 mark]