4. A road crosses a railway line at an angle of 30° as shown in following figure,
Find the values of a, b and c.
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Answer:
a=30
b=150
c=150
Step-by-step explanation:
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Similarly, p parallel to q and m is a transversal.
∴∠1=∠3=30
o
.... (2) [Corresponding angles]
∠a=∠3 [Vertically opposite angles]
∴∠a=30
o
[using 2]
In addition, p parallel to q and l is a transversal.
∴∠2=30
o
... [Corresponding angles]
Here, l is a straight line.
∴∠c+∠2=180
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[Linear pair]
∴30
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+∠2=180
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[by equation (2)]
⇒∠c=180
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−30
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⇒∠c=150
o
Therefore,
⇒∠a=30
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⇒∠b=150
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⇒∠c=150
o
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