In the adjoining figure, p || q. Find the unknown angles.
Solution:
We use the geometry concepts like parallel lines, alternate interior angles, supplementary angles, vertically opposite angles and adjacent angles to solve the problem.
Given p || q and it is intersected by a transversal.
∠𝑑 = 125°(corresponding angles)
125° + ∠𝑒 = 180°(Linear pair)
∠𝑒 = 180° - 125°
∠𝑒 = 55°
∠𝑒 = ∠f = 55°(vertically opposite angles)
∠𝑒 = ∠a = 55°(Corresponding angles)
∠𝑎 + ∠𝑏 = 180°(Linear pair)
55° + ∠𝑏 = 180°
∠𝑏 = 180° − 55°
∠𝑏 =125°
Also, ∠𝑏 = ∠𝑑 = 125°(Vertically opposite angles)
∠𝑎 = ∠𝑐 = 55°(Vertically opposite angles)
Thus, ∠𝑎 = 55°; ∠𝑏 = 125°; ∠𝑐 = 55°; ∠𝑑 = 125°; ∠𝑒 = 55° and ∠𝑓 = 55°.
☛ Check: NCERT Solutions Class 7 Maths Chapter 5
Video Solution:
In the adjoining figure, p || q. Find the unknown angles
NCERT Solutions for Class 7 Maths Chapter 5 Exercise 5.2 Question 3
Summary:
In the adjoining figure, p || q. The unknown angles are ∠𝑎 = 55°; ∠𝑏 = 125°; ∠𝑐 = 55°; ∠𝑑 = 125°; ; ∠𝑒 = 55° and ∠𝑓 = 55°.
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