Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![The image displays a geometry problem involving angles and a straight line.
### Diagram Details:
- The diagram consists of three lines forming angles at point 'a'.
- Angle `a` is labeled as 134°.
- An adjacent angle is denoted as `(3x - 2)°`.
- The lines form a straight angle, which means the angles add up to 180°.
### Angle Calculation:
To find the unknown angle `(3x - 2)°`, use the equation formed by the sum of these angles on a straight line:
\[ 134° + (3x - 2)° = 180° \]
### Solving the Equation:
1. Combine like terms:
\[ (3x - 2)° = 180° - 134° \]
2. Simplify the equation:
\[ (3x - 2)° = 46° \]
3. Solve for `x`:
\[ 3x - 2 = 46 \]
\[ 3x = 46 + 2 \]
\[ 3x = 48 \]
\[ x = 16 \]
### Answer Options:
- 98 Degrees
- 134 Degrees
- 52 Degrees
- 46 Degrees
### Conclusion:
The correct option would be 46 Degrees, as calculated for the angle \((3x - 2)°\).
### Graphs or Diagrams:
There are no graphs or additional diagrams in this image. The question relies on understanding angles and solving linear equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41246b41-0514-4655-8518-9db0e4990a43%2F7cf0110c-0303-43e8-915d-d1fa8d5ca1c2%2Fidxt2e_processed.jpeg&w=3840&q=75)
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