Question

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Answer 1

42) we use 4 properties to solve the above question-

a) alternate interior angles

b) exterior angles property of a triangle

c) angle sum property of a triangle

d) opp. angles property of a parallelogram

44) (i) since, diagonals of a parallelogram bisect each other,

therefore, 3x - 1= 2 (x + 1)

3x - 1= 2x + 2

3x - 2x = 2 + 1

So, x = 3

Similarly,

5y + 1= 6y - 1

1+1= 6y - 5y

So, y = 2

(ii) picture's not clear, but I think angle SRP = 40°

SO, y = 40° ( as since, opp. sides of a rhombus are parallel.... therefore alternate interior angles property is applied here)

Let the intersection point of diagonals be O.

Then, angle POQ = 90° ( since diagonals of a rhombus bisect each other at rt. angles)

therefore, using angle sum property of triangles,

angle PQS + 90° + 40° = 180°

angle PQS = 180° - 130° = 50°

Therefore, x = 50° ( alt. interior angle with angle PQS)