About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

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

Geometry: Master Shapes, Proofs & Spatial Reasoning

Angles and Lines

Angle relationships

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Parallel and perpendicular line segments

Identifying Parallel Lines

Identifying Perpendicular Lines

Perpendicular bisectors

Angle bisectors

Angle Bisectors

Coordinate Plane

Cartesian plane

Cartesian Plane — Coordinates

Draw on coordinate planes

Triangles

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Classifying Triangles

Isosceles and Equilateral Triangles

Circles

Angles in a circle

Chord properties 

Tangent properties

Circles and circumference 

Circle properties

Arcs of a circle

Areas and sectors of circles

Central angles and proofs

Inscribed angles and proofs

Central and inscribed angles in circles

Circle chord, tangent, and inscribed angles proofs

Surface Area and Volume

Volume of rectangular prisms word problems

Surface area of 3-dimensional shapes

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Introduction to volume

Calculate the Volume

Volume of prisms

Find the volume

Volume of Prisms Calculate Area and Volume

Rectangular Prisms Table

Volume of Prisms — Word Problem

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area of cylinders

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Transformations

Identifying vertices

Line symmetry

Rotational symmetry and transformations

Understanding tessellations

understand tessellations Interior Angle

Tessellations using translations and reflections

tessellations using translations and reflections

Tessellations using rotations

Introduction to transformations

Horizontal and vertical distances

Similarity

Similar solids

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Congruence

Congruence and congruent triangles

Triangles congruent by SSS proofs

Triangles congruent by SAS and HL proofs

Triangles congruent by ASA and AAS proofs

Logic

Inductive reasoning

Statements

Negations

Conjunctions and disjunctions

Truth tables

Conditionals

Inverses, converses, and contrapositives

Biconditionals

Deductive reasoning

Algebraic proofs

Reasoning

Consecutive integers

Number sequences

Finding the missing digit

math

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-geometry.png

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