what is the measure of angle RST? ### Geometry Quiz: Angle Measurement in Circles#### Question 2:**What is the measure of ∠RST?**(A) 51°(B) 62°(C) 67°(D) 102°#### Explanation with Diagram:In the provided diagram, a circle is drawn with points R, S, and T located on its circumference forming a triangle RST. The angle at R is marked as 67°. The arc between points R and S corresponds to a central angle measuring 102°.In a circle, the inscribed angle (∠RST in this case) subtended by the same arc is half the measure of the central angle subtended by that arc. Therefore, ∠RST can be calculated as:\[ \text{∠RST} = \frac{1}{2} \times 102° = 51° \]Thus, the correct answer is:(A) 51°#### Diagram Description:- A circle with points R, S, and T on its circumference.- ∠R measures 67°.- Arc RS corresponds to a central angle measuring 102°.

from the given figure we have to find the measure of S

Answered: what is the measure of angle RST?

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what is the measure of angle RST?

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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what is the measure of angle RST?

### Geometry Quiz: Angle Measurement in Circles

#### Question 2:
**What is the measure of ∠RST?**

(A) 51°

(B) 62°

(C) 67°

(D) 102°

#### Explanation with Diagram:
In the provided diagram, a circle is drawn with points R, S, and T located on its circumference forming a triangle RST. The angle at R is marked as 67°. The arc between points R and S corresponds to a central angle measuring 102°.

In a circle, the inscribed angle (∠RST in this case) subtended by the same arc is half the measure of the central angle subtended by that arc. Therefore, ∠RST can be calculated as:

\[ \text{∠RST} = \frac{1}{2} \times 102° = 51° \]

Thus, the correct answer is:

(A) 51°

#### Diagram Description:
- A circle with points R, S, and T on its circumference.
- ∠R measures 67°.
- Arc RS corresponds to a central angle measuring 102°.

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

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