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Master Angles in a Circle: Formulas, Rules, and Examples

NY.GEO-G.C.1

Central angles and proofs

NY.GEO-G.C.2a

Central and inscribed angles in circles

NY.GEO-G.C.2b

NY.GEO-G.C.5

auto-gen

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NY.GEO-G.CO.1

Line symmetry

Angles in a circle

Chord properties

Circles and circumference

Circle properties

Arcs of a circle

Areas and sectors of circles

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

NY.GEO-G.CO.10

Classifying triangles

Isosceles and equilateral triangles

NY.GEO-G.CO.11

Area and perimeter of parallelograms

2d shapes area and perimeter of parallelogram

2d shapes area and perimeter of parallelograms

NY.GEO-G.CO.12

Perpendicular bisectors

NY.GEO-G.CO.13

Inscribed angles and proofs

NY.GEO-G.CO.2

Rotational symmetry and transformations

Introduction to transformations

NY.GEO-G.CO.3

Horizontal and vertical distances

NY.GEO-G.CO.6

Congruence and congruent triangles

NY.GEO-G.CO.7

Triangles congruent by SSS proofs

NY.GEO-G.CO.8

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

NY.GEO-G.CO.9

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

NY.GEO-G.GMD.1

Surface area and volume of prisms

Surface area and volume of cylinders

Surface area and volume of cones

NY.GEO-G.GMD.3

Surface area and volume of pyramids

NY.GEO-G.GMD.4

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

NY.GEO-G.GPE.1a

Conics - Circle

NY.GEO-G.GPE.1b

NY.GEO-G.GPE.4

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Introduction to vectors

NY.GEO-G.GPE.5

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

NY.GEO-G.GPE.6

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

NY.GEO-G.GPE.7

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

NY.GEO-G.MG.1

Scale diagrams

NY.GEO-G.MG.2

Word problems of polynomials

NY.GEO-G.SRT.1

Enlargements and reductions with scale factors

NY.GEO-G.SRT.2

Similar triangles

NY.GEO-G.SRT.4

Pythagorean theorem

Pythagorean Theorem

Estimating square roots

Using the pythagorean relationship

Applications of pythagorean theorem

NY.GEO-G.SRT.5

Similar polygons

NY.GEO-G.SRT.6

Use sine ratio to calculate angles and sides (Sin = o / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

NY.GEO-G.SRT.7

Use cosine ratio to calculate angles and sides (Cos = a / h)

Cofunction identities

NY.GEO-G.SRT.8

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

NY.GEO-G.SRT.9

Area of triangles: 1/2 a*b sin(C)

math

Intro

- Hi, welcome to this question right here. So, in the following diagram which is here, the radius of the triangle is 24 centimeters, right? And we know the angle B, D, and C. That's this angle right here, is 75 degrees. So, we're trying to figure out the angle BAC, which is right over here. So, that's the missing angle that you're trying to figure out, okay? 
Now, there's a relationship between this angle and this angle. Now, the angle 75 is called the central angle. The central angle is called the C, for example, okay? 
And the inscribed angle of that central angle is only just half of that, okay? So, it's equal to the inscribed angle but you need to put a two times right there, okay? 
So, basically the central angle is double, double of the inscribed angle. Now, how do you know that one is really an inscribed while the other is the center? Well, the central angle is always from a point and then the other point, and they form with the center line, okay? The center point, okay? So, this is your central angle right here. Now, if you start and finish with the same points, which is B and C, and you form any triangle around your circle right here, those are called your inscribed angles, okay? Or they have the same arc lengths. You can actually look at the arc lengths right here. This is the arc length of the triangles, right? 
So, as long as they share the same arc length. Doesn't have to start from here to here. It could be somewhere else. As long as the arc length, the A-R-C, is the same. Therefore, this equation right here will exist, okay? The central angle is the double of the inscribed angle. So, if that's 75 over here, then, basically it's just two times the missing angle. Which is, let me put down. . . 
75 degrees and there's your two theta that's missing, okay? So, just grab your calculator and take the 75 divided by two, you get yourself the angle, which is this one right here, the BAC will just be 37.5 degrees. And that's your final answer for this question. Thanks for watching.

In a circle, chords, angles, inscribed angles and arc length all have special relationships with each other. This lesson focuses on exploring the relationships among inscribed angles in a circle as well as those of inscribed angle and central angle with the same arc. We will make use of the relationships to solve related questions in this lesson.  

Using formulas to find angles in a circle