Questions and Answers
How do you find the measure of each exterior angle of a polygon?
360 ÷ n =
What is the measure of each exterior angle of a regular 56-gon?
6.4
Given BE = 2x + 6 and ED = 5x - 12 in parallelogram ABCD, what is BD?
12
If the slope of PQ is 2/3 and the slope of QR is -1/2, what is the slope of SR for parallelogram PQRS?
Signup and view all the answers
Find angle W in parallelogram RSTW.
Signup and view all the answers
How do you find the sum of measures of interior angles of polygons?
Signup and view all the answers
What is the total interior angle measure of a quadrilateral?
Signup and view all the answers
If the angle measures are expressed as equations in a quadrilateral, how do you find x?
Signup and view all the answers
For parallelogram ABCD with angle A = 138, what is angle B?
Signup and view all the answers
Opposite sides of a parallelogram are always congruent.
Signup and view all the answers
What is the formula to find the number of angles in a polygon when given a total of angles?
Signup and view all the answers
How do you verify if a quadrilateral with given vertices is a parallelogram?
Signup and view all the answers
Study Notes
Exterior Angles of Polygons
- Measure of each exterior angle of a polygon: ( \frac{360}{n} ) where ( n ) is the number of sides.
- Example: Measure of each exterior angle of a regular 56-gon is ( 6.4^\circ ).
Parallelogram Properties
- In parallelogram ABCD, if given segments BE and ED, set equations equal for angle bisector: ( 2x + 6 = 5x - 12 ).
- Solving yields ( x = 6 ); substitute back to find length of BD.
Slope in Parallelograms
- For slopes PQ and QR, if PQ has slope ( \frac{2}{3} ) and QR has slope ( -\frac{1}{2} ), the slope of SR must equal that of PQ to maintain properties of a parallelogram.
Finding Angles in Parallelograms
- Angle W is congruent to angle S in parallelogram rstw. Solve for W using x, where ( W = S ) and ( x = 17 ).
Interior Angles of Polygons
- Total interior angles of a polygon: ( (n-2) \times 180 ).
- For a 48-gon, the total interior angles are ( (48-2) \times 180 = 8280^\circ ).
Quadrilateral Interiors
- Total interior angles of a quadrilateral is always 360°.
- Solve equations for each angle and substitute for ( x ) if required; consider if all angles need to be found or just ( x ).
Example of Solving for Angles
- Given ( 2x - 12 + 3x + 2 + x + 30 + x - 10 = 360 ), solve to find ( x = 50 ).
Angle Relationships in Parallelograms
- In parallelogram ABCD, if ( \angle A = 138^\circ ), then ( \angle B = 180 - 138 = 42^\circ ).
Parallelogram Identification
- A shape is a parallelogram if opposite sides are congruent and parallel. Use slope formula to check: ( \frac{y_2 - y_1}{x_2 - x_1} ) for opposite sides.
Angle Measure Example
- Angles L and J, given their measures, are congruent due to a bisector. Their totals relate to adjacent angles being supplementary to ( 180^\circ ).
Verifying Polygon Sides
- The number of angles in a polygon can be found inversely using: ( \frac{\text{given total}}{180} + 2 ). For 720°, this gives 6 sides; for 360°, it gives 4 sides.
General Tips for Geometry
- Always draw diagrams for clarity, label components, utilize calculators wisely, and confirm understanding of questions before solving.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Prepare for the Geometry Chapter 6 mid-chapter test with these flashcards. Learn how to find the measure of exterior angles of polygons and tackle example problems, including those related to parallelograms. This study aid emphasizes understanding the key concepts visually.
