Math, asked by singhaanjana699, 4 months ago

In the given figure, find the measure of ∠RQT, if PQ = QR and ∠QPR = 60°.





60°

140°

120°

100°

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Answers

Answered by AadityaSingh01
11

Given:- PQ = QR    and,    ∠QPR = 60°

Solution:- It can be solved through two methods.

Method 1:-

∠QPR = ∠QRP = 60°               [ PQ = QR,  Angle opposite to equal sides are equal ]

Now, ∠QPR + ∠QRP = ∠RQT              [ Exterior Angle Property of Triangles ]

⇒ 60°   +   60°  = ∠RQT

⇒ ∠RQT = 120°

Method 2:-

∠QPR = ∠QRP = 60°               [ PQ = QR,  Angle opposite to equal sides are equal ]

so, ∠QPR + ∠QRP + ∠PQR = 180°          [ Angle Sum Property of Δ ]

 ⇒ 60° + 60° + ∠PQR = 180°

 ⇒ 120° + ∠PQR = 180°

 ⇒ ∠PQR = 180° - 120°

 ⇒ ∠PQR = 60°

now, ∠PQR + ∠RQT = 180°             [ Linear Pair axiom ]

    ⇒ 60° + ∠RQT = 180°

    ⇒ ∠RQT = 180° - 60°

    ⇒ ∠RQT = 120°

∴ ∠RQT = 120°.

Some important terms:-

  • Sum of any two angles of any triangle is equal to the exterior opposite

angle of that triangle.

  • Sum of all interior angles of triangle is 180°.
  • Sum of all exterior angles of triangle is 360°.
  • Sum of all adjacent angles which is made on a straight line is of 180°.
Answered by anamikadasslp365
12

Answer:

exterior angle = sum of the two interior angle

angle QPR =60degree

=60+RQT=180(linear pair)

RQT=180-60=120

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