Question
In the given figure, the directed lines are parallel to each other. Find the unknown angles.
✓
Answer
∵ Lines are parallel
∴ q = t and p = 60° ..........(corresponding angles)
But t + 60° = 180° ........(linear pair)
⇒ t = 180°− 60° = 120°
t = r ........(vertically opposite angles)
∴ r = 120°
q = t = 120°
x = 110° .......(vertically opposite angles)
x + s = 180° .......(linear pair)
⇒ 110° + s = 180°
⇒ s = 180°− 110° = 70°
s = ∠1 ............(corresponding angles)
∴ ∠1 = 70°
y = ∠1 = 70° ........(vertically opposite angles)
Hence x = 110°, y = 70°, p = 60°, q = 120°, r = 120°, s = 70°, t = 120°
∴ q = t and p = 60° ..........(corresponding angles)
But t + 60° = 180° ........(linear pair)
⇒ t = 180°− 60° = 120°
t = r ........(vertically opposite angles)
∴ r = 120°
q = t = 120°
x = 110° .......(vertically opposite angles)
x + s = 180° .......(linear pair)
⇒ 110° + s = 180°
⇒ s = 180°− 110° = 70°
s = ∠1 ............(corresponding angles)
∴ ∠1 = 70°
y = ∠1 = 70° ........(vertically opposite angles)
Hence x = 110°, y = 70°, p = 60°, q = 120°, r = 120°, s = 70°, t = 120°
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