Question

In ΔABC, PQ || AB, ∠ACD = 150°.

∴ find x.

विकल्प

• 70°

• 110°

• 80°

• 30°

Answer 1

80°

Explanation:

We use the exterior angle theorem, which states:

The exterior angle of a triangle is equal to the sum of the two interior opposite angles.

In triangle ABC:

∠ACD is an exterior angle given as 150°,

PQ || AB implies that ∠ABC and ∠PQC are alternate interior angles, so they are equal.

Let:

∠ABC = x which is what we need to find,

∠CAB = y.

Then:

∠ACD = ∠ABC + ∠CAB = x + y.

Since ∠ACD = 150°, we have:

x + y = 150°.

Also, since ABC is a triangle:

x + y + ∠ACB = 180°,

So, ∠ACB = 180° – 150°

= 30°

Thus, the required angle x = ∠ABC = 80°.