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Question
In the following figure, PQ || RS and a : b = 3 : 2. Then, f is equal to ______.
Options
36°
108°
72°
144°
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Solution
In the following figure, PQ || RS and a : b = 3 : 2. Then, f is equal to 108°.
Explanation:
From the figure, PQ || RS.
From the question, it is given that, a : b = 3 : 2
So, let us assume a = 3m and b = 2m
We know that, the sum of angles on the straight line is equal to 180°
Then, ∠a + ∠b = 180°
3m + 2m = 180°
5m = 180°
m = `180^circ/5`
m = 36°
So, a = 3m = 3 × 36° = 108°
b = 2m = 2 × 36° = 72
Therefore, ∠a = ∠f = 108° ...[∵ Corresponding angles]
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