Question

Question 85

Bisect a straight angle, using ruler and compass. Measure each part.

Answer 1

Steps of construction are as follows:

Step I: Draw an angle $\angle ABC={180}^{\circ }$

Step II: With B as a centre and using a compass, draw an arc which cuts both rays of $\angle B$. Label point of intersection as P and Q.

Step III: With P as centre, draw an arc whose radius is more than half the length of PQ.

Step IV: With Q as centre and the same radius draw another arc. Let the two arcs intersect at D. Then $\overline{BD}$ is the required bisector of $\angle B$.

Thus, the required angles are $\angle ABD$ and $\angle CBD$.

On measuring,

$\angle ABD=\angle CBD={90}^{\circ }$