What is the measure of arc SQ? In this diagram, we have a circle with four points on its circumference labeled Q, R, S, and another point needing an angle measurement.### Diagram Description:1. **Chord RS** subtends an angle of 75° at the circumference on the opposite side from the center.2. There is another angle, ∠SQR, formed by the intersection of the chords SQ and QR. This angle measures 95°.3. An unknown angle at point Q is noted as "?" indicating that this angle measurement needs to be determined.### Detailed Explanation:The circle is divided by the chords into various segments and angles. The key relationships between these angles can be used to determine unknown measures.#### Key Concepts:- **Angles in the Same Segment**: Angles subtended by the same arc at the circumference are equal.- **Cyclic Quadrilateral Property**: The opposite angles of a quadrilateral that is inscribed in a circle (cyclic quadrilateral) sum up to 180°.Considering the cyclic quadrilateral QRSQ:- Opposite angles of a cyclic quadrilateral sum to 180°.- Given ∠QRS = 75°, and ∠SQR = 95°.Then, the unknown angle will be:- Calculate ∠QSR using the properties of cyclic quadrilaterals: The sum of ∠QRS and ∠QSR should equal 180°.- ∠QSR = 180° - 75° = 105°Hence, the unknown angle at point Q is 105°. This diagram visually represents the stated angle relationships and their properties in the context of a circle and helps in understanding geometrical principles related to cyclic quadrilaterals.

Name: What is the measure of arc SQ? In this diagram, we have a circle with
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: What is the measure of arc SQ? In this diagram, we have a circle with four points on its circumference labeled Q, R, S, and another point needing an angle measurement.### Diagram Description:1. **Chord RS** subtends an angle of 75° at the circumferen