###### Asked in Geometry

Geometry

# Do Inscribed angles have the same measure as their intercepted arcs?

## Answer

###### Wiki User

###### September 04, 2017 10:42AM

No they do not unless it is a circle with radius (180/pi) and the angles are measured in degrees, or a circle with radius (1/pi) and the angles are measured in radians.

## Related Questions

###### Asked in Geometry, Math and Arithmetic

### What is the relation between the arc length and angle for a sector of a circle?

A sector is the area enclosed by two radii of a circle and their
intercepted arc, and the angle that is formed by these radii, is
called a central angle.
A central angle is measured by its intercepted arc. It has the
same number of degrees as the arc it intercepts. For example, a
central angle which is a right angle intercepts a 90 degrees arc; a
30 degrees central angle intercepts a 30 degrees arc, and a central
angle which is a straight angle intercepts a semicircle of 180
degrees.
Whereas, an inscribed angle is an angle whose vertex is on the
circle and whose sides are chords. An inscribed angle is also
measured by its intercepted arc. But, it has one half of the number
of degrees of the arc it intercepts. For example, an inscribed
angle which is a right angle intercepts a 180 degrees arc. So, we
can say that an angle inscribed in a semicircle is a right angle; a
30 degrees inscribed angle intercepts a 60 degrees arc. In the same
or congruent circles, congruent inscribed angles have congruent
intercepted arcs.

###### Asked in Geometry

### The measure of an angle formed by two secants intersecting outside the circle equals?

The measure of the angle formed by two secants intersecting
outside the circle is one-half the difference of the intercepted
arcs.
Example:
Major intercepted arc is 200o and the minor intercepted arc is
120o.
1/2 (200-120) = 40o ...
The measurement of the angle formed by the two secants is
40o.
I HOPE THIS CAN HELP YOU :))

###### Asked in Geometry

### What is the measure of an angle formed by two secants intersecting outside the circle equals?

It is half the difference of the intercepted arcs.
Suppose you have a circle with centre O and the two secants AB
and CD, when extended meet at X which lies outside the circle.
Then the two arcs subtended by the secants are AC and BD. These
give the two angles as AOC and BOD and then the required angle is
0.5*(angle AOC - angle BOD).

###### Asked in Geometry

### What is the definition geometry conjecture?

Twenty Conjectures in Geometry:
Vertical Angle Conjecture: Non-adjacent angles formed by two
intersecting lines.
Linear Pair Conjecture: Adjacent angles formed by two
intersecting lines.
Triangle Sum Conjecture: Sum of the measures of the three
angles in a triangle.
Quadrilateral Sum Conjecture: Sum of the four angles in a
convex four-sided figure.
Polygon Sum Conjecture: Sum of the angles for any convex
polygon.
Exterior Angles Conjecture: Sum of exterior angles for any
convex polygon.
Isosceles Triangle Conjectures: Isosceles triangles have equal
base angles.
Isosceles Trapezoid Conjecture: Isosceles trapezoids have equal
base angles.
Midsegment Conjectures: Lengths of midsegments for triangles
and trapezoids.
Parallel Lines Conjectures: Corresponding, alternate interior,
and alternate exterior angles.
Parallelogram Conjectures: Side, angle, and diagonal
relationships.
Rhombus Conjectures: Side, angle, and diagonal
relationships.
Rectangle Conjectures: Side, angle, and diagonal
relationships.
Congruent Chord Conjectures: Congruent chords intercept
congruent arcs.
Chord Bisector Conjecture: The bisector of a chord passes
through the center of the circle.
Tangents to Circles Conjectures: A tangent to a circle is
perpendicular to the radius.
Inscribed Angle Conjectures: An inscribed angles has half the
measure of intercepted arc.
Inscribed Quadrilateral Conjecture: Opposite angles are
supplements.
The Number "Pi" Conjectures: Circumference and diameter
relationship for a circle.
Arc Length Conjecture: Formula to calculate the length of an
arc on a circle.

Load More