NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Problems and Solutions
Question 77

Question. 77

Draw an angle of 140° with the help of a protractor and bisect it using ruler and compasses.

Answer:

Construction: (1) Draw ∠XOY = 140° with protractor. (2) With centres X and Y on the arms and same radius, draw intersecting arcs at P. (3) Join OP; OP bisects the angle to 70° each.

Detailed Answer with Explanation:

Q77. Draw an angle of 140° with a protractor and bisect it using ruler and compasses.

Solution (Very Simple Steps)

Tools needed: Protractor, ruler (scale), pencil, pair of compasses, eraser.

Part A — Draw the 140° angle using a protractor

  1. Draw a straight ray and name it OX. This is one arm of the angle.
  2. Place the center hole of the protractor exactly on point O, with the baseline along ray OX.
  3. Look at the outer scale of the protractor (because we start from the ray). Find the mark for 140°.
  4. Put a small dot at the 140° mark.
  5. Remove the protractor and use the ruler to draw a ray from O passing through that dot. Name the new point on this ray as Y. Now you have angle ∠XOY.

(angle XOY = 140^circ)

Part B — Bisect (split into two equal parts) using compasses

  1. Keep the compass point on O. Open the compass to a small, comfortable width (any convenient width).
  2. Draw an arc that cuts both arms of the angle at two points. Mark these points as A on ray OX and B on ray OY.
  3. Without changing the compass width, place the compass point on A and draw a small arc inside the angle region.
  4. Now place the compass point on B (same width) and draw another small arc to cross the previous arc. Let the intersection be P.
  5. Use the ruler to draw a straight line from O to P. This line OP is the angle bisector.

(OP ext{ bisects } angle XOY)

(angle XOP = angle POY)

(angle XOP = angle POY = 70^circ)

Why this works (in simple words)

  • Points drawn from A and B with the same compass width are the same distance from both arms of the angle.
  • Their crossing point P is equally distant from the two arms.
  • All points that are equally distant from both arms lie on the angle bisector, so line OP must split the angle into two equal angles.

(PA = PB)

(Rightarrow P ext{ lies on the bisector of } angle XOY)

Check your result

  1. Place the protractor with center at O again.
  2. Measure ∠XOP and ∠POY. Each should be 70°.

(140^circ div 2 = 70^circ)

Answer: The line OP is the angle bisector, and it divides the angle into two equal angles of 70° each.

Tip: Keep the compass width the same while making the two small arcs from A and B. That’s the key to getting a perfect bisector.

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NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – Problems and Solutions | Detailed Answers