The Correct Answer and Explanation is:
The correct answer is 94°.
The problem presents a figure with two intersecting lines, k and m. When two lines intersect, they form angles at the point of intersection. The key to solving this problem lies in understanding the relationship between the angles that are adjacent to each other on a straight line.
These adjacent angles are called a linear pair. A linear pair of angles always adds up to 180 degrees because a straight line represents a straight angle, which has a measure of 180 degrees. Angles that sum to 180 degrees are also known as supplementary angles.
In the given figure, the angle with a measure of 86 degrees and the angle labeled ‘a’ are located next to each other along the straight line k. This means they form a linear pair and are supplementary.
To find the measure of angle ‘a’, we can set up an equation where the sum of the two angles equals 180 degrees:
86° + a = 180°
To isolate ‘a’ and find its value, we subtract 86 degrees from both sides of the equation:
a = 180° – 86°
Performing the subtraction gives us:
a = 94°
Therefore, the measure of angle ‘a’ is 94 degrees. This can be verified by noting that the four angles at the intersection consist of two pairs of equal, vertically opposite angles. The other two angles would be 86° and 94°, and the sum of all four (86 + 94 + 86 + 94) is 360 degrees, which is the total measure of angles around a point.
