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°
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly
(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play