in the given figure angel XYZ=56 and XY is produced to P. if ray YQ bisects Angel ZYP the measure of angel QYP=?
Answers
Step-by-step explanation:
XYZ=56 degree ( given)
QYZ=QYP (as QY is the bisector of angle ZYP)
XYZ + QYZ+QYP = 180 degree (linear pair)
XYZ +QYP+QYP= 180 degree ( as QYZ =QYP)
XYZ+ 2QYP=180 degree
56 degree + 2QYP= 180 degree
2QYP=180-56 degree
2QYP=124 degree
QYP=124/2
so QYP = 62 degree
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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.
Answer :-
i.e : XYP is a straight line.
∴ ∠XYZ + ∠ZYQ + ∠QYP = 180°
⇒ 64° + ∠ZYQ + ∠QYP = 180°
[∵ ∠XYZ = 64° (given)]
⇒ 64° + 2∠QYP = 180°
[YQ bisects ∠ZYP so, ∠QYP = ∠ZYQ]
⇒ 2∠QYP = 180° – 64° = 116°
⇒ ∠QYP = 116°/2 = 58°
∴ Reflex ∠QYP = 360° – 58° = 302°
Since ∠XYQ = ∠XYZ + ∠ZYQ
⇒ ∠XYQ = 64° + ∠QYP [∵∠XYZ = 64°(Given) and ∠ZYQ = ∠QYP]
⇒ ∠XYQ = 64° + 58° = 122° [∠QYP = 58°]
Thus, ∠XYQ = 122° and reflex ∠QYP = 302°.
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