# 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.

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