If L is the circumcentre of Δ XYZ and angle X is 40ᵒ, then the value of ∠YZL is:

If L is the circumcentre of Δ XYZ and angle X is 40ᵒ, then…

If L is the circumcentre of Δ XYZ and angle X is 40^o, then the value of ∠YZL is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e 50^o

Understanding

Application

We know that the angle subtended at the center is always double the angle subtended at the remaining arc.

When the two sides are equal in a triangle then the angles corresponding them will be equal

By the given property

⇒ 2∠YXZ = ∠YLZ

⇒ ∠YLZ = 2 × 40^o

⇒ 80^o

In triangle LYZ, the sum of all the angles = 180^o

⇒ ∠LYZ + ∠YZL + ∠YLZ = 180^o

⇒ 2∠YZL + 80^o = 180^o

⇒ ∠YZL = 50^o