NCERT Solutions for Class 8 Maths – Ganita Prakash
Exercise – 4.1
- Find all the other angles inside the followling rectangles.
(i) First Figure
Given: Angle at A = 30°
This is the angle between the bottom side (AB) and the diagonal.
Step 1: Find angle between diagonals
Since each diagonal makes the same angle with the base:
Angle between diagonals=2×30°=60°
Step 2: Use vertically opposite angles
At the intersection:
- One angle = 60°
- Opposite angle = 60°
- Remaining two angles = 180° − 60° = 120°
Step 3: Final answer (i)
- Small angles = 60°
- Big angles = 120°
(ii) Second Figure
Given: Angle between diagonals = 110°
Step 1: Find angle each diagonal makes with base
Angle with base=110°÷ 2 =55°
Step 2: Find other angles at intersection
- Opposite angle = 110°
- Remaining angles = 180° − 110° = 70°
Step 3: Final answer (ii)
- Angles with base = 55°
- Opposite angles = 110°
- Other angles = 70°
Draw a quadrilateral whose diagonals are equal in length (8 cm each), bisect each other, and intersect at an angle of:
(i) 30° (ii) 40° (iii) 90° (iv) 140°
Step-by-Step Construction (Example: 90° case)
- Draw a line segment AC = 8 cm
- Mark its midpoint O so that AO = OC = 4 cm
- At point O, draw a line perpendicular to AC (i.e., 90°)
- On this perpendicular line, mark points B and D such that:
- OB = OD = 4 cm
- Join A → B → C → D → A
✔️ You get the required quadrilateral
For Other Angles
Repeat the same steps, but in step 3, draw the angle as:
- 30° → for (i)
- 40° → for (ii)
- 140° → for (iv)
