Advertisements
Advertisements
Question
ABCD is a rectangle, if ∠BPC = 124°
Calculate:
- ∠BAP
- ∠ADP
Advertisements
Solution
Diagonals of rectangle are equal and bisect each other.
∠PBC = ∠PCB = x (say)
But ∠BPC + ∠PBC + ∠PCB = 180°
124° + x + x = 180°
2x = 180° – 124°
2x = 56°
⇒ x = 28°
∠PBC = 28°
But ∠PBC = ∠ADP [Alternate ∠s]
∠ADP = 28°
Again ∠APB = 180° – 124°
∠APB = 56°
Also, PA = PB
∠BAP = 12 (180° – ∠APB)
= 12 × (180°- 56°)
= 12 × 124°
= 62°
Hence, (i) ∠BAP = 62° (ii) ∠ADP = 28°
APPEARS IN
RELATED QUESTIONS
Explain why a rectangle is a convex quadrilateral.
ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)
In the following figure, ABCD and AEFG are parallelograms. If ∠C = 55°, what is the measure of ∠F?
Which of the following statement is true for a rectangle?
All rectangles are squares.
The sides of a rectangle are in the ratio 2 : 3, and its perimeter is 20 cm. Draw the rectangle.
The sides of a rectangle are in the ratio 4 : 5. Find its sides if the perimeter is 90 cm.
Show that the bisectors of angles of a parallelogram form a rectangle
Rectangle is a regular quadrilateral.
In a rectangle ABCD, AB = 25 cm and BC = 15. In what ratio does the bisector of ∠C divide AB?
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.
