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The supplement of angle K is 3 times the measure of angle K. Find the measure of angle K.

The supplement of angle K is 3 times the measure of angle K. Find the measure of angle K.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Unit 11 Exam** The problem statement is as follows: "The supplement of angle K is 3 times the measure of angle K. Find the measure of angle K." A prompt suggests, "Drawing a diagram may help." A text box is provided for entering the solution. **Explanation:** To solve the problem, recall that the supplementary angles add up to 180 degrees. If angle K is represented by \( x \), then its supplement is \( 180 - x \). According to the problem, the supplement of angle K is 3 times the measure of angle K. This can be set up as the equation: \[ 180 - x = 3x \] Solving for \( x \): 1. Add \( x \) to both sides: \[ 180 = 4x \] 2. Divide by 4: \[ x = 45 \] Therefore, the measure of angle K is \( 45 \) degrees.
Transcribed Image Text:**Unit 11 Exam** The problem statement is as follows: "The supplement of angle K is 3 times the measure of angle K. Find the measure of angle K." A prompt suggests, "Drawing a diagram may help." A text box is provided for entering the solution. **Explanation:** To solve the problem, recall that the supplementary angles add up to 180 degrees. If angle K is represented by \( x \), then its supplement is \( 180 - x \). According to the problem, the supplement of angle K is 3 times the measure of angle K. This can be set up as the equation: \[ 180 - x = 3x \] Solving for \( x \): 1. Add \( x \) to both sides: \[ 180 = 4x \] 2. Divide by 4: \[ x = 45 \] Therefore, the measure of angle K is \( 45 \) degrees.
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