It is given angle XYZ =64° and XY is produce to point P . Draw a figure from the given information . If ray YQ bisect and reflex angle QYP .
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Answer:
Ray YQ bisects ∠ZYP.
Let, ∠ZYQ = ∠QYP = a.
We can see from the figure that PX is a line and YZ is a ray intersecting at point Y and the sum of adjacent angles so formed is 180°.
Hence ∠ZYP + ∠ZYX = 180°
∠ZYQ + ∠QYP + ∠ZYX = 180° [Since, ∠ZYP = ∠ZYQ + ∠QYP]
a + a + 64° = 180°
2a + 64° = 180°
2a = 180° - 64° = 116°
a = 116°/2 = 58°
∴ Then ∠XYQ = ∠XYZ + ∠ZYQ
∠XYQ = a + 64°
⇒ ∠XYQ = 58° + 64° = 122°.
∠XYQ = 122°
As ∠QYP = a,
Thus, Reflex ∠QYP = 360° - a
⇒ 360° - 58° = 302°
Reflex ∠QYP = 302°.
Thus, we have ∠XYQ = 122° and Reflex ∠QYP = 302°.
Step-by-step explanation:
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