5. In the figure given below, m||n, TU||PQ and ∠SPQ=75ᵒ, ∠QOR =30ᵒ.
Find the angles∠ SOP, ∠ PQR, ∠TUQ & ∠STU.
Answers
Step-by-step explanation:
1 angle sop=angle qor=30. vertically opposite angles
2 angle spq=angle pqr=75. alternate interior angles
3 angle pqr=angle tuq=75 corresponding angles
4 angle qut+angle stu =180. co interior angles
75+angle stu=180
angle stu=105°
Given : m || n and TU||PQ
∠SPQ=75ᵒ, ∠QOR =30ᵒ.
To Find : ∠ SOP, ∠ PQR, ∠TUQ & ∠STU.
Solution:
∠QOR = 30°
∠SOP = ∠QOR ( Vertically opposite angles)
=> ∠SOP = 30°
∠PQR = ∠SPQ ( Alternate angle)
∠SPQ=75°
=> ∠PQR = 75°
∠TUQ = ∠PQR ( corresponding angles)
∠TUQ = 75°
∠STU + ∠SPQ = 180° Interior angles
=> ∠STU + 75° = 180°
=> ∠STU = 105°
Properties of angles formed by transversal line with two parallel lines :
• Corresponding angles are congruent.
• Alternate angles are congruent. ( Interiors & Exterior both )
• Interior angles are supplementary. ( adds up to 180°)
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