NCERT Solutions for Class 9 Maths Exercise 6.3

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NCERT solutions for Class 9 Maths Lines and Angles

NCERT Solutions for Class 9 Mathematics Lines and Angles

1. In the given figure, sides QP and RQ of ∆PQR are produced to points S and T respectively. If SPR = 135º and PQT = 110º, find PRQ.

Ans. We are given thatand .

We need to find the value ofin the figure given below.

From the figure, we can conclude thatform a linear pair.

We know that the sum of angles of a linear pair is.

and

and

Or,

From the figure, we can conclude that

(Angle sum property)

Therefore, we can conclude that.

NCERT Solutions for Class 9 Maths Exercise 6.3

2. In the given figure, X = 62º, XYZ = 54º. If YO and ZO are the bisectors of XYZ and XZY respectively of ∆XYZ, find OZY and YOZ.

Ans. We are given thatand YO and ZO are bisectors of, respectively.

We need to findin the figure.

From the figure, we can conclude that in

(Angle sum property)

We are given that OY and OZ are the bisectors of, respectively.

and

From the figure, we can conclude that in

(Angle sum property)

Therefore, we can conclude thatand.

NCERT Solutions for Class 9 Maths Exercise 6.3

3. In the given figure, if AB || DE, BAC = 35º and CDE = 53º, find DCE.

Ans. We are given that,.

We need to find the value ofin the figure given below.

From the figure, we can conclude that

(Alternate interior)

From the figure, we can conclude that in

(Angle sum property)

Therefore, we can conclude that.

NCERT Solutions for Class 9 Maths Exercise 6.3

4. In the given figure, if lines PQ and RS intersect at point T, such that PRT = 40º, RPT = 95º and TSQ = 75º, find SQT.

Ans. We are given that.

We need to find the value ofin the figure.

From the figure, we can conclude that in

(Angle sum property)

From the figure, we can conclude that

(Vertically opposite angles)

From the figure, we can conclude that in

(Angle sum property)

Therefore, we can conclude that.

NCERT Solutions for Class 9 Maths Exercise 6.3

5. In the given figure, if, PQ || SR,, then find the values of x and y.

Ans. We are given that.

We need to find the values of x and y in the figure.

We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”

From the figure, we can conclude that

, or

From the figure, we can conclude that

(Alternate interior angles)

From the figure, we can conclude that

(Angle sum property)

Therefore, we can conclude that.

NCERT Solutions for Class 9 Maths Exercise 6.3

6. In the given figure, the side QR of ∆PQR is produced to a point S. If the bisectors of meet at point T, then prove that.

Ans. We need to prove thatin the figure given below.

We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”

From the figure, we can conclude that in,is an exterior angle

…(i)

From the figure, we can conclude that in,is an exterior angle

We are given that are angle bisectors of

We need to substitute equation (i) in the above equation, to get

Therefore, we can conclude that the desired result is proved.

NCERT Solutions for Class 9 Maths Exercise 6.3

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