It is given that $ ∠$ XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects $∠$ ZYP, find $∠$ XYQ and reflex $∠$ QYP.

Question

It is given that  $ ∠$ XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects  $∠$ ZYP, find  $∠$ XYQ and reflex  $∠$ QYP.

cdquestions Admin · Accepted Answer

Given:   $∠$ XYZ = 64° and Ray YQ bisects  $∠$ PYZ. To Find:   $∠$ XYQ and Reflex  $∠$ QYP It can be observed that PX is a line. Rays YQ and YZ stand on it. Hence,  $∠$ XYZ + $∠$ ZYP = 180° By substituting,  $∠$ XYZ = 64°, we get 64° + $∠$ ZYP = 180° ∴  $∠$ ZYP = 116° As YQ bisects  $∠$ ZYP, $∠$ ZYQ =  $∠$ QYP Or  $∠$ ZYP = 2 $∠$ ZYQ ∴  $∠$ ZYQ =  $∠$ QYP = 58° Then  $∠$ XYQ =  $∠$ XYZ +  $∠$ ZYQ $∠$ XYQ = a + 64° $⇒$   $∠$ XYQ = 58° + 64° = 122°. $∠$ XYQ = 122° Now, reflex  $∠$ QYP = 180°+ $∠$ XYQ Since  $∠$ XYQ = 122° we have  ∠QYP = 180°+122° ∴  $∠$ QYP = 302°

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

It is given that \( ∠\)XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects \(∠\)ZYP, find \(∠\)XYQ and reflex \(∠\)QYP.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions