Question

An angle of $52.5°$can be constructed. Write True or False in each of the following. Give reasons for your answer.

• A. True
• B. False

Answer 1

The correct option is A True

Understand that by using a ruler and compass one can construct $30°$and $90°$ .

Know that every angle constructed with the help of a ruler and compass, angle bisector can be constructed.

Therefore,

$\begin{array}{c}52.5°=\frac{1}{2}\left(90°+\left(\frac{30°}{2}\right)\right)\\ =\frac{1}{2}(90°+15°)\\ =\frac{1}{2}\times 105°\\ =52.5°\end{array}$

Hence, the given statement is true.