Question

Draw $\angle PQR = 70^\circ $ using a protractor. Now using ruler and compasses, construct $\angle ABC = \angle PQR$.

Answer 1

Hint: This question is based on geometry construction and we have to draw an angle specified and then, using that angle, draw another one having the same value of degrees.
The tools required for the geometry construction are- a protractor, a ruler and a compass.

Complete step-by-step answer:
An $\angle PQR$ whose value in degrees is given as-
$\angle PQR = 70^\circ $
And another $\angle ABC$ having same value of degrees, so
$\angle ABC = \angle PQR$

The steps for the construction are given below -
(i) First step is to draw a horizontal line QP.
(ii) Then, taking point Q as the center, draw a line segment QR at an angle of $70^\circ $ using the protractor.
(iii) Now, using the compass, take some width assuming the point Q as the center and then draw an arc on the horizontal line QP, the arc intersects the line at point X.
(iii) Similarly, draw an arc QY on the line QR.
(iv) Now draw another horizontal line BM.
(v) Taking B as the center and keeping the same width as earlier, draw an arc BA on the line BM.
(vi) Also, draw another arc taking B as the center and now we have to find an intersection point of this arc.
(vii) To find the intersection of the arc, measure the distance XY using the ruler and then by using the compass, draw an arc at this distance, taking A as the center of this arc.
(viii) Join CB.
The value of this angle $\angle ABC$ would be same as $\angle PQR$
Therefore, $\angle ABC = \angle PQR$

Note: The steps of drawing the angle $\angle ABC$ is an alternate method of drawing an angle when we do not have the protractor. By using this method of construction, we can draw the angles at any given value of degrees.