Describing Angles

$$\begin{array}{r}{0}^{\circ }<m\angle A<90^{\circ }\end{array}$$ After we bisect $A,$ the resulting angles are identical and these angles will have a measure which is half as big as $m\angle A$. If $\angle B$ is one of the smaller angles, then the following is true. $$\begin{array}{r}\frac{0^{\circ }}{2}<m\angle B<\frac{90^{\circ }}{2}\Rightarrow 0^{\circ }<m\angle B<45^{\circ }\end{array}$$ Thus the two smaller angles will be acute.

$$\begin{array}{r}90^{\circ }<m\angle A<180^{\circ }.\end{array}$$ If we bisect $A,$ the angle is split into two identical angles that both have a measure half of $m\angle A.$ If we call one of the smaller angles $\angle B,$ then its measure will be in the following range. $$\begin{array}{r}\frac{90^{\circ }}{2}<m\angle B<\frac{180^{\circ }}{2}\Rightarrow 45^{\circ }<m\angle B<90^{\circ }\end{array}$$ An angle in that interval is acute.

$$\frac{180^{\circ }}{2}=90^{\circ }.$$ An angle with the measure $90^{\circ }$ is called a right angle.