Question

PLS HELP!!!!!!!!!!!!!!!!! DUE AT 3:00!!!

Angles LMN and OMP have the following measures: m∠LMN = (x 12)°, m∠OMP = (4x − 7)° Part A: If angle LMN and angle OMP are complementary angles, find the value of x. Show every step of your work. Part B: Use the value of x from Part A to find the measures of angles LMN and OMP. Show every step of your work. Part C: Could the angles also be vertical angles? Explain.

Answer 1

Angles LMN and OMP are complementary angles. The value of x is 17. The measures of angles LMN and OMP are 29 degrees and 61 degrees respectively.

Step-by-step explanation:

First, we need to understand the definition of complementary angles. Complementary angles are two angles whose measures add up to 90 degrees. In this case, we have angle LMN with a measure of (x + 12) degrees and angle OMP with a measure of (4x - 7) degrees. Since they are complementary angles, we can set up the equation (x + 12) + (4x - 7) = 90 and solve for x.

Simplifying the equation, we have 5x + 5 = 90. Subtracting 5 from both sides, we get 5x = 85. Dividing both sides by 5, we find that x = 17. Therefore, the value of x is 17.

For part B, we can substitute x = 17 into the given angle measures. Angle LMN = (x + 12) = 17 + 12 = 29 degrees. Angle OMP = (4x - 7) = (4 * 17 - 7) = 68 - 7 = 61 degrees.

For part C, vertical angles are two angles that share the same vertex and are formed by two intersecting lines. In this case, the angles LMN and OMP do not share the same vertex and are not formed by intersecting lines. Therefore, they are not vertical angles.

Answer 2

To find the value of x for complementary angles LMN and OMP, we solve the equation (x + 12)° + (4x - 7)° = 90°, yielding x = 17. This gives us m∠LMN = 29° and m∠OMP = 61°. These angles cannot be vertical angles because they are not equal.

Step-by-step explanation:

To solve for the value of x when angles LMN and OMP are complementary angles, we set up an equation given that the sum of complementary angles is 90 degrees:

1. m∠LMN + m∠OMP = 90°.
2. (x + 12)° + (4x - 7)° = 90°.
3. Combine like terms: 5x + 5 = 90.
4. Subtract 5 from both sides: 5x = 85.
5. Divide by 5: x = 17.

With the value of x found, we can determine the measure of the two angles:

1. m∠LMN = (x + 12)° = (17 + 12)° = 29°.
2. m∠OMP = (4x - 7)° = (4(17) - 7)° = 61°.

As for Part C, LMN and OMP could also be vertical angles if they are opposite angles formed by two intersecting lines. However, since vertical angles are equal and LMN and OMP are not equal (29° ≠ 61°), in this case, they cannot be vertical angles.