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:
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