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Pachacha [2.7K]
2 years ago
14

Answer this correctly please BRAINLIEST+HEART+5 STARS ko yung matinong answer

Mathematics
1 answer:
Ann [662]2 years ago
5 0

Applying the triangle inequality theorem and the exterior angle theorem, we have:

1. m∠1 > m∠3

2. MI > IX

3. 3 < MX < 27

4. m∠4 = 115°

<h3>What is the Triangle Inequality Theorem?</h3>

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side of that triangle.

<h3>What is the Relationship of Sides to Interior Angles in a Triangle?</h3>

The longest side is opposite to the largest interior angle while the shortest side of the triangle is always directly opposite the shortest interior angle in that triangle.

<h3>What is the Exterior Angle Theorem?</h3>

The exterior angle theorem states that the sum of the opposite angles to an exterior angle in a triangle equals the measure of that exterior angle.

1. The angles of a triangle are relative to the length of their opposite sides. Therefore, if MI which is relative to ∠1 is 15 and IX which is relative to ∠3 is 12, it implies that m∠1 is greater than m∠3.

2. Given, m∠1 = 65° and is relative to side MI, and m∠3 = 50° and is relative to side IX, therefore, side MI is longer or greater than side IX.

3. Given, MI = 15; IX = 12, based on the triangle inequality theorem, the measure of MX would be determined as shown below:

15 - 12 < MX < 15 + 12

3 < MX < 27

4. Given, m∠2 = 65°; m∠3 = 50°. Based on the exterior angle theorem, we have:

m∠4 = m∠2 + m∠3

Substitute

m∠4 = 65 + 50

m∠4 = 115°

Learn more about the triangle inequality theorem on:

brainly.com/question/309896

#SPJ1

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