Question

Question 87

Draw an angle ABC of measure ${45}^{\circ }$, using ruler and compass. Now draw and $\angle DBA$ of measure ${30}^{\circ }$ using ruler and compass as shown in the figure, What is the measure of $\angle DBC$?

Answer 1

To draw an angle, we use following steps of construction:

Step I: Draw a line segment BC of any length.

Step II: Place the compass pointer at B and draw a right angle ${90}^{\circ }$

Step III: Draw the angle bisector of the right angle, such that $\angle ABC=\frac{1}{2}\left({90}^{\circ }\right)={45}^{\circ }$

Step IV: Place the compass pointer at B and draw an angle of ${30}^{\circ }$ on the base BA $\angle DBA$

Step V: By the help of protractor, we get $\angle DBC={75}^{\circ }$