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.
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**Figure ABCD is a parallelogram.**
**What is the value of x?**
- A) 6
- B) 7
- C) 8
- D) 9
In the image, there is a diagram of a parallelogram ABCD with vertices labeled A, B, C, and D going clockwise starting from the top left corner.
- Side AB is parallel and equal in length to side CD.
- Side AD is parallel and equal in length to side BC.
On the diagram:
- The length of side AD is given as \(5x + 3\).
- The length of side BC is given as 38.
**Explanation of the Diagram:**
The properties of a parallelogram dictate that opposite sides are equal in length. Therefore, in this diagram, we set the length of side AD equal to the length of side BC:
\[ 5x + 3 = 38 \]
To find the value of \(x\), solve the equation:
\[ 5x + 3 = 38 \]
\[ 5x = 38 - 3 \]
\[ 5x = 35 \]
\[ x = \frac{35}{5} \]
\[ x = 7 \]
The value of \(x\) is \(7\).
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