Question

Given that m∠ZL=12x+45 and m∠M=18x–30, determine the measure of each angle.

A) m∠ZL=12(45)+45 degrees, m∠M=18(45)–30 degrees
B) m∠ZL=12(30)+45 degrees, m∠M=18(30)–30 degrees
C) m∠ZL=12(15)+45 degrees, m∠M=18(15)–30 degrees
D) m∠ZL=12(60)+45 degrees, m∠M=18(60)–30 degrees

Answer 1

The correct answer is option D) m∠ZL=12(60)+45 degrees, m∠M=18(60)–30 degrees.

Thus option d is correct.

Explanation:

The problem provides the angle measures in terms of variables x. To find the values of these angles, set the given expressions equal to each other and solve for x. So, according to the problem:

m∠ZL = 12x + 45

m∠M = 18x – 30

Equating these two expressions:

12x + 45 = 18x – 30

Now, solve for x:

12x + 45 = 18x – 30

Combine like terms:

12x - 18x = -30 - 45

-6x = -75

x = -75 / -6

x = 12.5

Now that we have found x, substitute it back into the expressions to find the measures of the angles:

m∠ZL = 12x + 45 = 12(12.5) + 45 = 150 + 45 = 195 degrees

m∠M = 18x – 30 = 18(12.5) – 30 = 225 – 30 = 195 degrees

Therefore, m∠ZL = 195 degrees and m∠M = 195 degrees. This aligns with option D) m∠ZL=12(60)+45 degrees, m∠M=18(60)–30 degrees, providing the correct measures for the given angles.

Therefore option d is correct.