Find all the other angles inside the following rectangles. Class 8

Find all the other angles inside the following rectangles. Class 8

Question 1.

Find all the other angles inside the following rectangles. Class 8

Solution:

(i) ∠OBA = ∠OAB = 30°.

So, ∠AOB = 180° - (30° - 30°) = 120°

⇒ ∠COD = 120°

∠AOD = 180° - 120° = 60°

⇒ ∠BOC = 60°

∠ODA = ∠OAD = [latex]\frac{180^{\circ}-60^{\circ}}{2}[/latex] = 60°

Similarly, ∠OBC = ∠OCB = 60° and ∠ODC = ∠OCD = 30°

(ii) ∠PTS = 110°

So, ∠TPS = ∠TSP = [latex]\frac{180^{\circ}-110^{\circ}}{2}[/latex] = 35°

Also, ∠PTQ = 180° - 110° = 70°

So. ∠TPQ = ∠TQP = [latex]\frac{180^{\circ}-70^{\circ}}{2}[/latex] = 5

Similarly, ∠TQR = ∠TRQ = 35°

and ∠TSR = ∠TRS = 55°.

Question 2.

Consider a circle with centre O. Line segments PL and AM are two perpendicular diameters of the circle. What is the figure APML? Reason and/or experiment to figure this out. Class 8

Solution:

PAML is a square. Because PL = AM and ∠MOL = 90°.