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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### Question 4
**Find x**
8.
*Figure Description*:
The image depicts two right triangles that are combined to form a larger right triangle.
1. The left triangle has a right angle at the bottom left corner, and an angle of 28° adjacent to this right angle.
2. The right triangle has a right angle at the bottom right corner, and an unknown angle x° adjacent to this right angle.
Note: The two triangles share the hypotenuse of the larger right triangle.
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Explanation:
To find the value of angle x:
- We know that the sum of angles in any triangle is 180°.
- In the larger right triangle, the combination of the smaller right triangles gives three angles, one of which is the right angle (90°). Thus, for the larger triangle:
\[ 28° + x° + 90° = 180° \]
- Simplifying this equation:
\[ 28° + x° = 90° \]
\[ x° = 90° - 28° \]
\[ x° = 62° \]
So, the value of angle x is 62°.
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Given figure is
We know that if two lines intersect , then vertically opposite angles are equal.
Therefore,
Also, sum of all angles of a triangle is 180 degrees.
So,
Step by step
Solved in 3 steps with 3 images
