Do the diagonals of a parallelogram intersect at a particular angle? Class 8

Do the diagonals of a parallelogram intersect at a particular angle? Class 8

Question 1.

Do the diagonals of a parallelogram intersect at a particular angle? Class 8

Solution:

No.

Question 2.

Find the remaining angles in the following quadrilaterals. Class 8

Solution:

(i) ∠E = 180° - 40° = 140°, ∠A = ∠P = 40°, and ∠R = ∠E = 140°.

(ii) ∠S = 180° - 110° = 70°, ∠Q = ∠S = 70°, and ∠R = ∠P = 110°.

(iii) ∠UXY = ∠UVX = 30°

So, ∠XUV = 180° - 30° - 30° = 120°

∠WXV = ∠UVX = 30°

So, ∠WVX = ∠WXV = 30°

Hence, ∠XWV = 120°.

(iv) ∠AOE = ∠AEO = 20°

So, ∠OAE = 180° - 20° - 20° = 140°,

∠IOE = ∠AEO = 20°,

∠IEO = ∠IOE = 20°

and so ∠OIE = 140°.