Question

Draw an angle of ${70^ \circ }$. Make a copy of it using only a straight edge and compasses.

Answer 1

Hint: To draw the angle of ${70^ \circ }$, simple draw a ray and with the use of protractor draw an angle $\angle BAC = {70^ \circ }$. In order to copy this angle , draw a ray PQ , with the help of compass draw an arc with any radius centre at A which cut AB at D and AC at E. With same radius draw an arc on PQ ray, which cut PQ at R. Measure the length of DE with the compass and with same length marks an arc having pointed end of compass at R which cut the previous arc at S. Join PS. $\angle QPS$ is your required angle.

Complete step by step solution:
In our question, our objective is to first draw the angle of ${70^ \circ }$ and then make the copy of it using only straight line edges and compasses.
Let’s first draw an angle of ${70^ \circ }$
Now to draw the angle of ${70^ \circ }$ we will be using protractor
Follow the below steps to draw an angle of ${70^ \circ }$
Step 1: Draw a ray AB on a plain white sheet with the help of a ruler and sharp pointed pencil.

Step 2: Now place the centre of the protector at A and let the line AB coincide with the line of the protector.
Step 3: Mark a point C on ${70^ \circ }$.
Step 4: Join the AC
.

Step 5: You have successfully obtained an angle of ${70^ \circ }$i.e. $\angle BAC = {70^ \circ }$
Now let's make a copy of this angle $\angle BAC$
Follow the below steps:
Step 1. Draw a ray PQ on a plain white sheet with the help of a ruler and sharp pointed pencil.
Step 2.From point A, draw an arc of any radius intersecting the ray AB at point D and AC at E.
Step 3.Now using the compass open the same length, as in step 2 and draw an arc by taking point P as centre which cut the ray PQ at point R
Step 4. Now back on to the original angle $\angle BAC$ and open the length of the compass equal to DE.
Step 5.Keeping the radius of the compass same. Put the pointed end of the compass on the point R and mark an arc which cuts the previous arc at point S.
Step 6. Join PS.
Step 7. you have successfully copied the angle $\angle BAC$ as $\angle QPS$.

Note: 1.Draw the cartesian plane only with the help of straight ruler and pencil to get the perfect and accurate results.
2.Mark the points carefully.
3. Use the compass very carefully and steady. Your hand should not shake while drawing any arc or radius.