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Geometry. **The exterior angle of a triangle will always be greater than the two remote interior angles**. In other words, the measure of the red angle is greater than that of the blue angle or the green angle.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.Which best describes the exterior angle inequality theorem? A. **The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles**.

## What is the exterior angle equality theorem?

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.

## Which best describes the exterior angle inequality theorem?

Which best describes the exterior angle inequality theorem? A. **The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles**.

### Exterior Angle Inequality Theorem With Two Column Proofs – Geometry

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## What is the definition of triangle inequality theorem?

triangle inequality, in Euclidean geometry, **theorem that the sum of any two sides of a triangle is greater than or equal to the third side**; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

## How do you find an exterior angle?

The formula for calculating the size of an exterior angle is: **exterior angle of a polygon = 360 ÷ number of sides**.

## How do you find the exterior angle of a triangle with variables?

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**.

## What is exterior angle geometry?

Definition of exterior angle

1 : **the angle between a side of a polygon and an extended adjacent side**. 2 : an angle formed by a transversal as it cuts one of two lines and situated on the outside of the line.

### EXTERIOR ANGLE INEQUALITY THEOREM || GRADE 8 MATHEMATICS Q4

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### Theorems of Inequality – Video & Lesson Transcript | Study.com

The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than both of the non-adjacent …

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The Exterior Angle Theorem states that: An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The following diagram shows the …

### Inequalities in Triangles

Theorem: An exterior angle at A of triangle ABC is great than either of the (interior) angles B or C. Proof: For the proof, construct this figure. M is the …

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The Exterior Angle Inequality theorem states that an exterior angle of a triangle is greater than either of the remote interior angles.

## What is the relationship between the measure of the exterior angle of a triangle and its remote interior angles?

The exterior angle theorem states that: **The measure of an exterior angle of a triangle is supplementary to its adjacent interior angle**. The sum of the remote interior angles must equal the measure of the exterior angle of the triangle.

## What theorem states that the measure of an exterior angle of a triangle is greater than the measure of either interior angle?

**The exterior angle theorem** is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

## What are the 4 triangle inequality theorems?

The 3 properties of the triangle inequality theorem are: **If the sum of any two sides is greater than the third, then the difference of any two sides will be less than the third**. The sum of any two sides must be greater than the third side. The side opposite to a larger angle is the longest side in the triangle.

## How does the triangle inequality theorem relate to angles?

Theorem 36: **If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite the greater side**.

### Exterior Angle Inequality Theorem

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## Which of the following is the statement of the triangle inequality theorem?

**The sum of the lengths of any two sides of a triangle is greater than the length of the third side**.

## What is the sum of exterior angle of a triangle?

A triangle is a three-sided polygon with three sides, three vertices, and three edges. The exterior angle of a triangle is defined as the angle formed between one of its sides and its adjacent extended side. The sum of exterior angles of a triangle is equal to **360 degrees**.

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