Advertisements
Advertisements
Question
PQRS is a rectangle. The perpendicular ST from S on PR divides ∠S in the ratio 2:3. Find ∠TPQ.
Advertisements
Solution
Given, ST ⊥ PR and ST divides ∠S in the ratio 2:3
So, sum of ratio = 2 + 3 = 5
Now, `∠TSP = 2/5 xx 90^circ = 36^circ, ∠TSR = 3/5 xx 90^circ = 54^circ`
Also, by the angle sum property of a triangle,
∠TPS = 180° – (∠STP + ∠TSP)
= 180° – (90° + 36°)
= 54°
We know that, ∠SPQ = 90°
⇒ ∠TPS + ∠TPQ = 90°
⇒ 54° + ∠TPQ = 90°
⇒ ∠TPQ = 90° – 54° = 36°
APPEARS IN
RELATED QUESTIONS
The angle between the altitudes of a parallelogram, through the same vertex of an obtuse angle of the parallelogram is 60°. Find the angles of the parallelogram.
In the following figure, BDEF and DCEF are each a parallelogram. Is it true that BD = DC? Why or why not?
In a rectangle ABCD, prove that ∆ACB ≅ ∆CAD.
Find the length of the diagonal of a rectangle whose sides are 12 cm and 5 cm.
Diagonals of a rectangle ABCD intersect at point O. If AC = 8 cm then find BO and if ∠CAD =35° then find ∠ACB.
The interior angle made by the side in a parallelogram is 90° then the parallelogram is a
If the adjacent angles of a parallelogram are equal, then the parallelogram is a ______.
A rectangular MORE is shown below:
Answer the following questions by giving appropriate reason.
- Is RE = OM?
- Is ∠MYO = ∠RXE?
- Is ∠MOY = ∠REX?
- Is ΔMYO ≅ ΔRXE?
- Is MY = RX?
A line l is parallel to line m and a transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y interesct at P and Q. Is PXQY a rectangle? Given reason.
Construct a rectangle whose one side is 3 cm and a diagonal equal to 5 cm.
