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:
Given: ∠XYZ = 64° and Ray YQ bisects ∠PYZ.
To Find: ∠XYQ and Reflex ∠QYP
When a ray intersects a line, the sum of adjacent angles formed is 180°.
With the given information in the question, we can come up with this diagram.
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°.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 6
Video Solution:
It is given that ∠XYZ = 64º and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.
NCERT Solutions Class 9 Maths Chapter 6 Exercise 6.1 Question 6:
Summary:
If ∠XYZ = 64°, XY is produced to point P, and tay YQ bisects ∠ZYP, then ∠XYQ= 122° and reflex ∠QYP= 302°.
☛ Related Questions:
- In Fig. 6.29, if AB || CD, CD || EF and y : z = 3 : 7, find x.
- In Fig. 6.30, if AB||CD, EF ⊥ CD and ∠GED =126°, find ∠AGE, ∠GEF and ∠FGE.
- In Fig. 6.31, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.[Hint: Draw a line parallel to ST through point R.]
- In Fig. 6.32, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.