Final answer:
The plain text measures of the complementary angles LMN and UVW, given the expressions (3x + 5)° and 2x° for their measures, are 56° and 34°, respectively.
Step-by-step explanation:
Solving for Complementary Angles
Given that angles LMN and UVW are complementary, this means that their measures add up to 90 degrees. This can be represented by the equation ∠LMN + ∠UVW = 90°. Substituting the given measures of the angles into this equation, we have (3x + 5)° + 2x° = 90°.
Now, we can solve for 'x': Combining like terms gives us 5x + 5 = 90. Subtracting 5 from both sides of the equation, we get 5x = 85. Dividing both sides by 5, we find x = 17.
Substituting x = 17 back into the angle expressions, we have the measure of ∠LMN = (3*17 + 5)° = 56° and the measure of ∠UVW = 2*17° = 34°. Therefore, the plain text measure of angle LMN is 56° and of angle UVW is 34°.
Learn more about Complementary Angles