In the given figure, find the measure of ∠RQT, if PQ = QR and ∠QPR = 60°.
60°
140°
120°
100°
Answers
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°.
Answer:
exterior angle = sum of the two interior angle
angle QPR =60degree
=60+RQT=180(linear pair)
RQT=180-60=120