7 th maths chapter 5 || 5.4

7th Standard Mathematics — Chapter 5: Geometry

Exercise 5.4 Solutions (Construction of Angle Bisectors)

1. Construct the following angles using protractor and draw a bisector to each of the angle using ruler and compass.

(a) Angle = 60°

Steps of Construction:

1. Draw a ray BC with vertex B using a ruler.
2. Place the protractor center at B, align the baseline along ray BC, and mark point A at 60°. Draw ray BA to form ∠ABC = 60°.
3. With center B and any convenient radius, draw an arc cutting ray BA at P and ray BC at Q.
4. With center P and radius greater than half of PQ, draw an arc in the interior of ∠ABC.
5. With center Q and the same radius, draw another arc intersecting the previous arc at point E.
6. Join ray BE. Ray BE is the required angle bisector of ∠ABC, making ∠ABE = ∠EBC = 30°.

(b) Angle = 100°

Steps of Construction:

1. Draw ray BC with vertex B.
2. Using a protractor at B, mark point A at 100° and draw ray BA.
3. With center B, draw an arc intersecting BA at P and BC at Q.
4. With centers P and Q and radius > ¹/₂ PQ, draw intersecting arcs at point E.
5. Join ray BE to bisect ∠ABC into two 50° angles (∠ABE = ∠EBC = 50°).

(c) Angle = 90°

Steps of Construction:

1. Draw ray BC with vertex B.
2. Using a protractor, measure and mark 90° at point A. Draw vertical ray BA.
3. With center B, draw an arc cutting BA at P and BC at Q.
4. With centers P and Q, draw arcs of equal radius intersecting at point E.
5. Draw ray BE to bisect the right angle into two 45° angles (∠ABE = ∠EBC = 45°).

(d) Angle = 48°

Steps of Construction:

1. Draw ray BC with vertex B.
2. Using a protractor at B, mark point A at 48° and draw ray BA.
3. With center B, draw an arc cutting BA at P and BC at Q.
4. With centers P and Q, draw two arcs intersecting at point E in the interior of the angle.
5. Draw ray BE to bisect ∠ABC into two equal 24° angles (∠ABE = ∠EBC = 24°).

(e) Angle = 110°

Steps of Construction:

1. Draw ray BC with vertex B.
2. Using a protractor at B, mark point A at obtuse angle 110° and draw ray BA.
3. With center B, draw an arc cutting BA at P and BC at Q.
4. With centers P and Q and radius > ¹/₂ PQ, draw two arcs intersecting at point E.
5. Draw ray BE to bisect ∠ABC into two 55° angles (∠ABE = ∠EBC = 55°).