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

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

test

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

Solving two-step linear equations using distributive property: a(x + b) = c

Solve Linear Equations Using Distributive Property – Word Problem

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

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

Surface area of cylinders

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

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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

Central angles and proofs

Inscribed angles and proofs