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.
![### Question 2
#### Find the measure of \( x \)
**6.**
- The question presents two triangles with given angle measures.
1. **First triangle:**
- This triangle has two labeled angles. One of the angles is labeled as \( x^\circ \) (unknown angle to be found). Another angle has no measure marked.
2. **Second triangle:**
- This triangle has its angles partially labeled as well. One angle is marked as \( 64^\circ \), and the other angle at the top vertex seems to be the same angle present in the first triangle.
### Educational Explanation
The diagram helps to visualize and practice the method of solving for angle measures in triangles. To find the measure of \( x \) in the first triangle, we can follow these steps:
1. **Recognize that the angle at the vertex in both triangles are the same**:
This is implicit by the fact that both triangles are presented in similar orientation, implying a shared angle measurement.
2. **Use the property of angles in a triangle**:
The sum of the angles in any triangle is \( 180^\circ \).
3. **Calculate missing angles in the second triangle**:
\[
\text{Let the unknown angle at the top be } y.
\]
\(
y + 64^\circ + \text{(third angle)} = 180^\circ
\)
By concluding that the angles in both triangles are proportional and similar, it assists in recognizing the measure of unknown angles by given values. Employing these principles will yield the measure of \( x^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20047395-754f-4b4f-b55f-051358973abe%2Fd134f498-ae67-4381-9c42-4c3e67f25f70%2Fxfn2wvp.jpeg&w=3840&q=75)
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