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.
Solve for x.
![This diagram represents a circle with two angles, one of which is 116°. The circle is divided into two segments by a straight line extending from the boundary of the circle through its center. The angle of 116° is clearly marked on one side of the line, while the other angle is denoted by \( x^\circ \).
To find the value of \( x \), we can use the fact that the sum of angles around a point is 360°. Specifically, in this case, since \( 116° \) and \( x \) form a linear pair and lie on a straight line through the center of the circle, their sum should equal 180°.
So, to solve for \( x \):
\[ 116° + x = 180° \]
Subtracting 116° from both sides gives:
\[ x = 180° - 116° \]
\[ x = 64° \]
Therefore, the value of \( x \) is \( 64° \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa61fad0-ceb7-416c-8279-8e32da5d69e0%2F7ee09a7d-dbf9-4ed8-b933-2abb141ba398%2Fa2ktw98_processed.png&w=3840&q=75)
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