Question

In circle T with m_SVU = 15, find the mZSTU.

HELPP!

Answer 1

`m\angle STU=30^\circ`

Explanation:

Angles in a Circle

There are many theorems that relate angles inside and outside a circle.

To solve this question we need to recall the relation of any central angle and a subtended angle by the same arc.

The image below explains this relationship:

Central angle (2x) is twice any inscribed angle (x) subtended by the same arc (marked in red).

The image provided in the question shows an arc US subtended by the inscribed angle SVU and the central angle STU.

If we know the measure of the angle SVU as 15°, then the angle STU must be twice 15°, i.e., 30°.

`\mathbf{m\angle STU=30^\circ}`