How to find the exterior angle of a triangle
There are angles on the outside, too!
Nov 20, · 4 Short Steps for answering Exterior Angle of a Triangle Example Problems The three angles in a triangle add up to degrees. The degree measure of a straight line add up to degrees. If you are given the adjacent angle you subtract the angle from degrees to solve for the exterior angle of. Exterior Angle Theorem. The measure of an exterior angle (our w) of a triangle equals to the sum of the measures of the two remote interior angles (our x and y) of the triangle. Let's try two example problems. Example A: If the measure of the exterior angle is (3x - 10) degrees, and the measure of the two remote interior angles are 25 degrees and (x + 15) degrees, find x.
The exterior angle of a triangle is the angle formed between one side and the extension of its adjacent side. States the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite or non-adjacent interior angles.
Here, we will apply the exterior angle theorem to find the missing interior or exterior angles in a triangle. Your email address will not be published.
Save my name, email, and website in this browser for the next time I comment. All rights reserved. Reproduction in whole or in part without permission is how to make mayo sauce. Table of Contents. Last modified on April 22nd, What is the Exterior Angle of a Triangle The exterior angle of a triangle is the angle formed between one side and the extension of its adjacent side.
How to Find Exterior Angles of a Triangle Here, we will apply the anglw angle theorem to find the missing interior or exterior angles in a triangle. Solve for x. Calculate values of x and y in the given trizngle. Leave a Reply Cancel reply Your email address will not be published. Worksheets Hexagon Worksheets. Square Shape Worksheets. Rhombus Worksheets. Simplifying Fractions Worksheets. Similar Polygons Worksheets.
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Exterior Angles and Interior Angles
An exterior angle of a triangle is equal to the sum of the two opposite interior angles, thus an exterior angle is greater than any of its two opposite interior angles; for example, in ?ABC, ?5 = ?a + ?b. The sum of an exterior angle and its adjacent interior angle is equal to degrees; for example, ?5 + . For a triangle: The exterior angle d equals the angles a plus b. The exterior angle d is greater than angle a, or angle b. Exterior Angle of a Triangle An exterior angle of a triangle is formed when one side of a triangle is extended. The nonstraight angle (the one that is not just the extension of the side) outside the triangle, but adjacent to an interior angle, is an exterior angle of the triangle (Figure 1). Figure 1 Exterior angle of a .
See picture below. We can use equations to represent the measures of the angles described above. One equation might tell us the sum of the angles of the triangle. For example,. We know this is true, because the sum of the angles inside a triangle is always degrees. What is w? We don't know yet. Notice how Z and W together make a straight line?
That's degrees. So, we can make a new equation:. Here's how to do that:. This tells us that the measure of the exterior angle equals the total of the other two interior angles. In fact, there is a theorem called the Exterior Angle Theorem which further explores this relationship:. The measure of an exterior angle our w of a triangle equals to the sum of the measures of the two remote interior angles our x and y of the triangle.
Note that here I'm referring to the angles W, X, and Y as shown in the first image of this lesson. Their names are not important. What is important is that an exterior angle equals the sum of the remote interior angles. Remember that "x" is not the answer here.
The angles, then, are 65, 25, and 40 degrees. The exterior angle given is degrees. Find x. Calculating the Angles We can use equations to represent the measures of the angles described above. We're given the exterior angle
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