Question

MO bisects ZLMN, m∠LMN = (7x - 24), and m∠ZNMO = (2x + 31). Solve for x and find m∠LMO, m∠ZOMN, and m∠LMN. A) x = 10, m∠LMO = 13°, m∠ZOMN = 51°, m∠LMN = 42° B) x = 14, m∠LMO = 12°, m∠ZOMN = 53°, m∠LMN = 38° C) x = 16, m∠LMO = 14°, m∠ZOMN = 55°, m∠LMN = 36° D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°

Answer 1

To solve for x and find the measures of the angles in the triangle, set the expressions for the angles equal to each other and solve for x. Substituting the value of x back into the expressions, we can find the measures of each angle. Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

Step-by-step explanation:

To solve for x and find the measures of the angles, we can set the expressions for the angles equal to each other and solve for x.

Equating the expressionsGeometry or the angles, we have:

7x - 24 = 2x + 31

5x = 55

x = 11

Substituting x = 11 into the expressions for the angles, we can find:

m∠LMO = 7(11) - 24 = 47°

m∠ZOMN = 2(11) + 31 = 53°

m∠LMN = 7(11) - 24 = 47°

Therefore, the correct answer is Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

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Answer 2

To solve for x and find the measures of the angles in the triangle, set the expressions for the angles equal to each other and solve for x. Substituting the value of x back into the expressions, we can find the measures of each angle. Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

Step-by-step explanation:

To solve for x and find the measures of the angles, we can set the expressions for the angles equal to each other and solve for x.

Equating the expressionsGeometry or the angles, we have:

7x - 24 = 2x + 31

5x = 55

x = 11

Substituting x = 11 into the expressions for the angles, we can find:

m∠LMO = 7(11) - 24 = 47°

m∠ZOMN = 2(11) + 31 = 53°

m∠LMN = 7(11) - 24 = 47°

Therefore, the correct answer is Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

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Answer 3

To solve for x and find the measures of the angles in the triangle, set the expressions for the angles equal to each other and solve for x. Substituting the value of x back into the expressions, we can find the measures of each angle. Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

Step-by-step explanation:

To solve for x and find the measures of the angles, we can set the expressions for the angles equal to each other and solve for x.

Equating the expressionsGeometry or the angles, we have:

7x - 24 = 2x + 31

5x = 55

x = 11

Substituting x = 11 into the expressions for the angles, we can find:

m∠LMO = 7(11) - 24 = 47°

m∠ZOMN = 2(11) + 31 = 53°

m∠LMN = 7(11) - 24 = 47°

Therefore, the correct answer is Option D) x = 12, m∠LMO = 15°, m∠ZOMN = 49°, m∠LMN = 45°.

Learn more about Geometry