Question

The sum of the measures of the angles shown is 114. Which choice is the measure of angle n?

a) 42
b) 48
c) 57
d) 66

Answer 1

The measure of angle (n) is 66 degrees (option D)

Step-by-step explanation:

Let's denote the angles in the figure as follows:

- The angle in the bottom-left corner as (A)

- The angle in the bottom-right corner as (B)

- The angle in the top-right corner as (C)

According to the information given, the sum of these angles is 114 degrees:

[A + B + C = 114]

We are asked to find the measure of angle (n), which is adjacent to angles (A) and (C). Since angles (A) and (C) together form a straight line (180 degrees), we have:

[A + n + C = 180]

Now, we can substitute the first equation into the second:

[114 + n = 180]

Solving for (n):

[n = 180 - 114 = 66]

Therefore, the measure of angle (n) is 66 degrees (option D).

Answer 2

The measure of angle n is 66 degrees, thus the correct option is d.

Step-by-step explanation:

In the given figure, several angles are depicted, and their sum totals 114 degrees. To determine the measure of angle n, begin by identifying angles that are congruent or supplementary within the figure. Based on geometric properties, angles n and m form a linear pair and are supplementary angles. A linear pair of angles adds up to 180 degrees. Thus, since the total sum of angles is given as 114 degrees, subtracting this from 180 degrees gives the measure of angle n as 66 degrees (option d).

Therefore, by recognizing the relationship between angles n and m as a supplementary pair, subtracting the total sum from 180 degrees provides the measure of angle n as 66 degrees. This approach adheres to the principles of angle relationships and supplementary angles within geometric figures, allowing us to ascertain the precise measure of angle n in the given scenario.