Question

ZA and B are complementary. If MZA = (6x – 15)° and m2B = (3x + 6)°, find x, MLA, and mzB.

Options:
A) x = 5, MLA = 75°, mzB = 21°
B) x = 10, MLA = 45°, mzB = 36°
C) x = 15, MLA = 60°, mzB = 27°
D) x = 20, MLA = 30°, mzB = 42°

Answer 1

To find x, MLA, and mzB, use the fact that ZA and B are complementary angles. Set up an equation, solve for x, and substitute the value of x to find MLA and mzB.

Step-by-step explanation:

To find x, MLA, and mzB, we need to use the fact that ZA and B are complementary angles. Complementary angles add up to 90 degrees. So, we have:

MZA + mzB = 90

Substituting the given values:

(6x - 15) + (3x + 6) = 90

Combining like terms:

9x - 9 = 90

Adding 9 to both sides:

9x = 99

Dividing both sides by 9:

x = 11

Now, we can find MLA and mzB by substituting the value of x:

MLA = 6x - 15 = 6(11) - 15 = 66 - 15 = 51°

mzB = 3x + 6 = 3(11) + 6 = 33 + 6 = 39°