If TP and TQ are the two tangents to a circle with centre O so that , then  is equal toA 60º B 70º C 80º D 90º

1. Break Down the Problem

We need to find the angle $\angle POQ$ given two tangents $TP$ and $TQ$ drawn from a point $T$ to a circle with center $O$.

2. Relevant Concepts

From geometry, we know that:

• The angle between the tangents from a point outside a circle is equal to the angle formed at the center of the circle by the radii to the points of tangency.
• If $TP$ and $TQ$ are tangents from point $T$ to points $P$ and $Q$ on the circle, then $\angle POQ = 2\alpha$, where $\alpha$ is the angle formed by the tangents.

3. Analysis and Detail

The angle formed between two tangents from an external point is equal to the supplementary angle of the angle at the center: $\angle POQ + 2\alpha = 180^\circ$ This means we have: $\angle POQ = 180^\circ - 2\alpha$

However, without specific values or an associated diagram, we can use the typical values that could apply based on common angle measures associated with tangents.

4. Verify and Summarize

With possible options given (A: 60º, B: 70º, C: 80º, D: 90º), we need to ascertain which angle would be plausible for tangents to meet with specific angles at point $T$.

To deduce:

• $90^\circ$ is a common angle at which tangents meet at $T$ due to symmetry, indicating $45^\circ$ angles up to $O$—suggesting $\frac{180^\circ}{2} = 90^\circ$.

Final Answer

The angle $\angle POQ$ is $\boxed{90^\circ}$.