Exercise 12.1
1. In quadrilateral PQRS
Answer:
(i)
(i) Name the sides, angles, vertices and diagonals.
Sides:
Angles: ∠
Vertices:
Diagonals:
(ii)
(ii) Name all the pairs of adjacent sides, adjacent angles, opposite sides and opposite angles.
Adjacent sides:
PQ and
QR and
RS and
SP and
Adjacent angles:
∠P and ∠
∠Q and ∠
∠R and ∠
∠S and ∠
Opposite sides:
PQ and
QR and
Opposite angles:
∠P and ∠
∠
2. The three angles of a quadrilateral are 60°, 80° and 120°. Find the fourth angle?
Answer:
Sum of all angles in a quadrilateral =
Let the fourth angle =
x° = 360° - 260° =
Therefore, the fourth angle is
3. The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the measure of each of the four angles.
Answer:
Let the angles be
Sum of angles =
2x° + 3x° + 4x° + 6x° = 360°
x° =
The four angles are:
First angle = 2x° = 2(24°) =
Second angle = 3x° = 3(24°) =
Third angle = 4x° = 4(24°) =
Fourth angle = 6x° = 6(24°) =
4. The four angles of a quadrilateral are equal. Draw this quadrilateral in your notebook. Find each of them.
Answer:
Let each angle =
Since sum of angles = 360°
x° + x° + x° + x° = 360°
x° =
Each angle =
This quadrilateral is a
5. In a quadrilateral, the angles are x°, (x + 10)°, (x + 20)°, (x + 30)°. Find the angles.
Answer:
Sum of angles = 360°
x° + (x + 10)° + (x + 20)° + (x + 30)° =
x + x + 10 + x + 20 + x + 30 = 360
4x =
x =
The four angles are:
First angle = x° =
Second angle = (x + 10)° =
Third angle = (x + 20)° =
Fourth angle = (x + 30)° =
6. The angles of a quadrilateral cannot be in the ratio 1 : 2 : 3 : 6. Why? Give reasons.
Answer:
Let the angles be
Sum of angles =
x° + 2x° + 3x° + 6x° = 360°
x° =
The angles would be:
Why this is impossible:
An angle of
Reason: In any quadrilateral, each interior angle must be