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

Advertisements
Advertisements

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

Advertisements

Solution

Using angle sum property for ΔPRT, we obtain

∠PRT + ∠RPT + ∠PTR = 180º

40º + 95º + ∠PTR = 180º

∠PTR = 180º − 135º

∠PTR = 45º

∠STQ = ∠PTR = 45º (Vertically opposite angles)

∠STQ = 45º

By using angle sum property for ΔSTQ, we obtain

∠STQ + ∠SQT + ∠QST = 180º

45º + ∠SQT + 75º = 180º

∠SQT = 180º − 120º

∠SQT = 60º

  Is there an error in this question or solution?
Chapter 6: Lines and Angles - Exercise 6.3 [Page 107]

APPEARS IN

NCERT Mathematics Class 9
Chapter 6 Lines and Angles
Exercise 6.3 | Q 4 | Page 107

RELATED QUESTIONS

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


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


In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR = 1/2∠QPR.


Find the value of the unknown x in the following diagram:


Find the value of the unknowns x and y in the following diagram:


In the given figure find m∠P.


In the following triangle, find the value of x


In the following triangle, find the value of x


In the following triangle, find the value of x


In the following triangle, find the value of x


Two line segments `bar("AD")` and `bar("BC")` intersect at O. Joining `bar("AB")` and `bar("DC")` we get two triangles, ∆AOB and ∆DOC as shown in the figure. Find the ∠A and ∠B


In ∆RST, ∠S is 10° greater than ∠R and ∠T is 5° less than ∠S, find the three angles of the triangle


In ∆ABC, if ∠B is 3 times ∠A and ∠C is 2 times ∠A, then find the angle


In the given figure, which of the following statement is true?


If ∆MNO ≅ ∆DEF, ∠M = 60° and ∠E = 45° then find the value of ∠O


In ∆DEF, ∠F = 48°, ∠E = 68° and bisector of ∠D meets FE at G. Find ∠FGD


If one angle of a triangle is equal to the sum of the other two angles, then the triangle is ______.


An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is ______.


If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be ______.


How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.


The angles of a triangle are in the ratio 2:3:4. Find the angles of the triangle.


A triangle ABC is right-angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL = ∠ACB.


Prove that a triangle must have atleast two acute angles.


In the figure, ∠Q > ∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM = `1/2` (∠Q – ∠R).


In a right-angled triangle, the angles other than the right angle are ______.


If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is ______.


The measure of three angles of a triangle are in the ratio 5:3:1. Find the measures of these angles.


Find the values of x and y in the given figure.


The angles of a triangle are arranged in descending order of their magnitudes. If the difference between two consecutive angles is 10°, find the three angles.


In the given figure, find the values of x, y and z.


Share
Notifications



      Forgot password?
Use app×