**Find the value of the variable or the measure of the numbered angle in circle $ \bigoplus P $.****Problem 40:**A circle with a center labeled $ P $. There is one triangle inscribed in the circle. The top angle of the triangle is exterior to the circle and measures $ 37^\circ $. The bottom-left angle of the triangle, which is interior to the circle, is labeled as angle $ 1 $.**Problem 41:**A circle with a center labeled $ P $. There are two intersecting chords in the circle. The intersection point forms an angle at the circumference, labeled $ (33x + 3)^\circ $, and an arc opposite the angle at the circumference, measuring $ 204^\circ $.---To solve these problems, you will need to understand properties of inscribed angles, exterior angles, and arcs in circle geometry:**For Problem 40:**Use the known relationship between the exterior angle of a triangle and the opposite interior angles to find the measure of angle $ 1 $.**For Problem 41:**Use the properties of angles formed by intersecting chords and their corresponding arcs to find the value of $ x $.

Find the variable x OR the Numbered Angle. (40) Find 1 (41) Find x

Answered: Find the value of the variable or the…

Math

Geometry

Find the value of the variable or the measure of the numbered angle in OP. 40. 41. 37 (33x + 3) 204

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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Question

**Find the value of the variable or the measure of the numbered angle in circle $ \bigoplus P $.**

**Problem 40:**

A circle with a center labeled $ P $. There is one triangle inscribed in the circle. The top angle of the triangle is exterior to the circle and measures $ 37^\circ $. The bottom-left angle of the triangle, which is interior to the circle, is labeled as angle $ 1 $.

**Problem 41:**

A circle with a center labeled $ P $. There are two intersecting chords in the circle. The intersection point forms an angle at the circumference, labeled $ (33x + 3)^\circ $, and an arc opposite the angle at the circumference, measuring $ 204^\circ $.

---

To solve these problems, you will need to understand properties of inscribed angles, exterior angles, and arcs in circle geometry:

**For Problem 40:**
Use the known relationship between the exterior angle of a triangle and the opposite interior angles to find the measure of angle $ 1 $.

**For Problem 41:**
Use the properties of angles formed by intersecting chords and their corresponding arcs to find the value of $ x $.

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