Question

what conjecture can you make about the measure of the base angles in the nth triangle in the pattern? not to scale
a. 180 - 2n
b. $\frac{180 - 2n}{2}$
c. $\frac{180(n - 1)}{2}$
d. $\frac{180 - n}{2}$

Explanation:

Step1: Observe the pattern of the base - angle measures

The base - angle measures in the given triangles are 89°, 88°, 87°, 86° for the 1st, 2nd, 3rd, 4th triangles respectively. The measure of each base - angle is decreasing by 1° as the triangle number \(n\) increases by 1.

Step2: Find the general formula

The first base - angle measure is 89°. We can express 89 as \(\frac{180 - 2\times1}{2}\), the second (88) as \(\frac{180-2\times2}{2}\), the third (87) as \(\frac{180 - 2\times3}{2}\), and the fourth (86) as \(\frac{180-2\times4}{2}\).
For the \(n\)th triangle, the measure of each base - angle is given by the formula \(\frac{180 - 2n}{2}\).

Answer:

B. \(\frac{180 - 2n}{2}\)