Up

Inscribed angles

Before we begin, let’s state a few important theorems.

THEOREM:  If two angles inscribed in a circle intercept the same arc, then they are equal to each other.

THEOREM:  If an angle inside a circle intercepts a diameter, then the angle has a measure of \(90^\circ \).

Now let’s use these theorems to find the values of some angles!

 

EXAMPLE:  Find the measure of the angle indicated.

Circles-Inscribed-Angles-1

SOLUTION:  First we see that \(\measuredangle DNC\) and \(\measuredangle DEC\) both intercept the same arc.  So, by our first theorem, we know that \(\measuredangle DNC = \measuredangle DEC\). And since \(\measuredangle DNC = 37^\circ \), we conclude that \(\measuredangle DEC = 37^\circ \).

Next, since \(\measuredangle EDC\) intercepts a diameter of the circle, we can conclude, by our second theorem, that \(\measuredangle EDC = 90^\circ \).

So two of the angles in triangle \(EDC\) are \(90^\circ \) and \(37^\circ \). Then, by using the fact that the tree angles of a triangle must sum to \(180^\circ \), we know that the measure of the desired angle is \(53^\circ \).

EXAMPLE:  Find the measure of the indicated angle.

Circles-Inscribed-Angles-2

SOLUTION:  Since \(\measuredangle NBM\) and \(\measuredangle NLM\) intercept the same arc, they are equal, so that \(\measuredangle NLM = 52^\circ \). Next, since \(\measuredangle NML\) intersects a diameter of the circle, we know that \(\measuredangle NML = 90^\circ \). Then since two of the angles of triangle \(LMN\) are \(90^\circ \) and \(52^\circ \), we know that the desired angle must be \(38^\circ \), by the fact that the three angles of a triangle must sum to \(180^\circ \). Solution:  The desired angle is \(38^\circ \).

Below you can download some free math worksheets and practice.


Downloads:
5121 x

State if each angle is an inscribed angle. If it is, name the angle and the intercepted arc.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Circles-Inscribed-angles-Easy

Watch bellow how to solve this example:

 

Downloads:
4178 x

Find the measure of the arc or angle indicated.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Circles-Inscribed-angles-Medium

Watch bellow how to solve this example:

 

Downloads:
4582 x

Solve for x and y.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Circles-Inscribed-angles-Hard

Watch bellow how to solve this example:

 
 
 

Facebook PageGoogle PlusTwitterYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems