Question

In the following figure, PQ || RS and a : b = 3 : 2. Then, f is equal to ______.

Options

• 36°

• 108°

• 72°

• 144°

Answer 1

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]