What theorem states that the measure of an exterior angle
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The exterior angle theorem is one of the most fundamental theorems of triangles. Before we begin the discussion, let us have a look at what a triangle is. A polygon is defined as a plane figure bounded by a finite number of line segments to form a closed figure. Triangle is the polygon bounded by a least number of line segments, i.e. three. It has three edges and three vertices. Figure 1 below represents a triangle with three sides AB, BC, CA, and three vertices A, B and C. ∠ABC, ∠BCA and ∠CAB are the three interior angles of ∆ABC. Show
 Fig. 1 Triangle ABC One of the basic theorems explaining the properties of a triangle is the exterior angle theorem. Let us discuss this theorem in detail. Statement: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles. Fig. 2 Exterior Angle Theorem The above statement can be explained using the figure provided as: According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠CAB would be equal to the exterior angle ∠ACD. General proof of this theorem is explained below: Proof: Consider a ∆ABC as shown in fig. 2, such that the side BC of ∆ABC is extended. A line, parallel to the side AB is drawn as shown in the figure. Fig. 3 Exterior Angle Theorem
Thus, from the above statements, it can be seen that the exterior ∠ACD of ∆ABC is equal to the sum of two opposite interior angles i.e. ∠CAB and ∠ABC of the ∆ABC. Hence proved. To know more about triangles and the properties of triangles, download BYJU’S-The Learning App from Google Play Store. Frequently Asked Questions – FAQsThe below formulas can be stated from the exterior angle theorem. According to the exterior angle inequality theorem, the measure of an exterior angle of a triangle is greater than either of its interior opposite angles. If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles. Yes, the sum of exterior angles in a polygon is always added up to 360 degrees. The sum of the measures of the exterior angles of any triangle is 360 degrees. Image credit: Desmos Before we cover the exterior angle theorem, let's review a few definitions.
We'll use the above triangle to demonstrate the exterior angle theorem's principles:
Breaking Down the Exterior Angle TheoremLet's look at how the exterior angle theorem works. First, let’s review the angle sum theorem, which states that the interior angles of a triangle equal 180°. Image credit: Desmos In the above triangle ECD, the exterior angle of DEF and its adjacent interior angle CED are linear pairs. That means together, they form a straight line and equal 180°. Because these two adjacent angles add to 180° and the interior measures of the angles of a triangle also equal 180°, the sum of the remote interior angles ECD and CDE must equal the measure of exterior angle DEF. Next, we'll use this knowledge to find angle measurements. Applying the Exterior Angle TheoremLet's use the exterior angle theorem in the triangle below: Image credit: Desmos Since we know that the angle EST = 125° and the adjacent interior angle TSU is its supplementary angle, let's solve for the measure of this interior angle: Now let's use the second part of the exterior angle theorem: The exterior angle equals the sum of the remote interior angles. We'll follow this logic and find the remote interior angle TUS by subtracting STU from EST: Understanding Exterior and Interior AnglesThe exterior angle theorem states that:
This theorem can help you solve for missing angles and understand the relationship between exterior and interior angles within a triangle. More Math Homework Help:
What theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles of the triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles.
What is the statement of exterior angle theorem?Statement: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
What theorem justifies the statement the measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angle?Triangle Exterior Angle Theorem – Corollary
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
What theorem states that the exterior angle of a triangle is equal to the sum of two remote interior angles of the triangle Brainly?This is Expert Verified Answer
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.
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