In Figure, lines XY and MN intersect at O. If $∠$POY=90° and a:b=2:3, find c.

Question

In Figure, lines XY and MN intersect at O. If  $∠$ POY=90° and a:b=2:3, find c.

cdquestions Admin · Accepted Answer

Given:  $∠$ POY= 90° and a: b = 2: 3. Let the common ratio between a and b be x. ∴ XY is a straight line, rays OM and OP stand on it. ∴ $∠$ POY =  $∠$ POX = 90° $∠$ POX = ∠POM +  $∠$ MOX 90° = a + b Now, a = 2x and b = 3x $⇒ $ a + b = 90° 2x + 3x = 90° 5x = 90° x =  $\frac{90°}{5}$  = 18° a = 2x = 2  $×$  18° a = 36° b = 3x = 3 × 18° b = 54° Also,  $∠$ MOY=  $∠$ MOP +  $∠$ POY = a + 90° = 36° + 90° = 126° ∴ c = 126º

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

In Figure, lines XY and MN intersect at O. If \(∠\)POY=90° and a:b=2:3, find c.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions