Answer :
We know Measures of angles complementary, supplementary, vertical, and adjacent angles, we use the given equation:
x = 14(90-x) and solve for x.
The solution is x = 84, so the measure of the angle is 84 degrees and its complementary angle is 6 degrees. To find the measures of complementary, supplementary, vertical, and adjacent angles, we need to understand the relationships between these angles. Complementary angles add up to 90 degrees. Let the measure of one angle be x. The measure of its complementary angle is 90-x.
According to the problem, the measure of an angle is fourteen times the measure of its vertical angle.
So, we have the complementary equation x = 14(90-x).
Solving the equation gives x = 14(90-x),
x = 1260/15,
x = 84.
Therefore, the measure of the angle is 84 degrees and its complementary angle is 90-84 = 6 degrees.
To know more about Measures of angles visit:
https://brainly.com/question/14684647
#SPJ11
The measures of the complementary angles are 6 degrees and 84 degrees. This is found by setting up and solving the equation x + 14x = 90. Additional concepts involving angles include supplementary, vertical, and adjacent angles.
Let's solve for the measure of each angle given that the measure of an angle is fourteen times the measure of its complementary angle.
Step 1: Define complementary angles: Two angles are complementary if their measures add up to 90 degrees.
Step 2: Let the measure of the smaller angle be x. Then, the measure of its complementary angle is 14x.
Step 3: Set up the equation for complementary angles:
x + 14x = 90
15x = 90
Step 4: Solve for x:
x = 90 ÷ 15
x = 6
Step 5: Find the measure of each angle: The smaller angle is 6 degrees, and the larger angle is 14 × 6 = 84 degrees.
Therefore, the measures of the angles are 6 degrees and 84 degrees, which are complementary angles.
Additional definitions for clarity:
- Supplementary angles: Two angles whose measures add up to 180 degrees.
- Vertical angles: Angles formed by two intersecting lines that are congruent.
- Adjacent angles: Angles that share a common vertex and side, but do not overlap.
