Bisecting Angles: Divide and Conquer in Geometry

Question:

If an angle KM bisects angle JKL and angle JKM is 86 degrees, what is the measure of angle JKL?

Answer:

The measure of angle JKL is 172 degrees.

When a line bisects an angle, it divides the angle into two equal parts. In this case, if angle JKM is given as 86 degrees, then because KM bisects JKL, the other part of the divided angle will also be 86 degrees. So, the total angle JKL equals 86 + 86 = 172 degrees, leading to Option 4 as the correct answer.

Explanation:

In geometry, when a line bisects an angle, it divides the angle into two equal smaller angles - JKM and MKL. Since the measure of angle JKM is 86 degrees, the measure of angle MKL is also 86 degrees because KM bisects JKL. By adding the measures of the two smaller angles (86 degrees + 86 degrees), we get the total measure of angle JKL as 172 degrees. Therefore, the correct answer is Option 4: 172.

Understanding how angles are bisected can help in solving various geometry problems and applications. It's an important concept to grasp for further studies in mathematics.