In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?
Given:
Angle STR =
Ratio of Angle P to Angle Q = 4 : 5
Formula Used:
In a quadrilateral, the angle formed by the intersection of bisectors of two adjacent angles is half the sum of the other two angles.
Solution:
Substitute the given value into the formula.
Let \angle P = 4x and \angle Q = 5x.
Difference between and = 5x - 4x = x =
Final Answer
So the correct answer is (d)
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90 Mins English English100 Questions100 Marks90 Mins English English100 Questions100 Marks90 Mins EnglishIn quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?
In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?
There is a polygon of 10 sides. How many triangles can be drawn using the vertices of the polygon?
P is any point inside the rectangle ABCD. If PA = 87 cm, PB = 12 cm and PC = 96 cm, then the length of PD (in cm) is equal to:
In the given figure, ABCD is a square. Angle DEC = 75 degrees. What is the value (in degrees) of angle EFA?
In the given figure, what is value (in degrees) of Q?
Let ABCD be a quadrilateral which satisfies any of the following conditions.
( i ) opposite sides are equal
( ii ) each diagonal of ABCD divides it into congruent triangles
( iii ) each pair of opposite angles are equal
( iv ) diagonals of ABCD bisect each other
Then ABCD has to be a _____________
How many diagonals can be there in a regular polygon with 37 sides?
A parallelogram is a quadrilateral in which:
The number of diagonals in a hexagon is :
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Suggested Test Series
In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?
In quadrilateral PQRS, the bisectors of ∠R and ∠S meet at the point T (inside the quadrilateral) and ∠STR = 22.5°. If the ratio of ∠P to ∠Q is 4 : 5, then what is the difference between the measures of ∠Q and ∠P?
There is a polygon of 10 sides. How many triangles can be drawn using the vertices of the polygon?
P is any point inside the rectangle ABCD. If PA = 87 cm, PB = 12 cm and PC = 96 cm, then the length of PD (in cm) is equal to:
In the given figure, ABCD is a square. Angle DEC = 75 degrees. What is the value (in degrees) of angle EFA?
In the given figure, what is value (in degrees) of Q?
Let ABCD be a quadrilateral which satisfies any of the following conditions.
( i ) opposite sides are equal
( ii ) each diagonal of ABCD divides it into congruent triangles
( iii ) each pair of opposite angles are equal
( iv ) diagonals of ABCD bisect each other
Then ABCD has to be a _____________
How many diagonals can be there in a regular polygon with 37 sides?
A parallelogram is a quadrilateral in which:
The number of diagonals in a hexagon is :
