Two adjacent angles form a straight angle. One angle measures 4 times the measure of the other. What is the measure, in degrees, of the smaller angle?
For angle problems involving straight lines, first recall that a straight angle measures . Represent one angle with a variable (usually the smaller one), express the other angles in terms of that variable using the given relationships (like “4 times as large”), and then write an equation where their sum is . Solve the simple linear equation and double-check by adding the two angle measures to ensure they total and that you are giving the angle the problem specifically asks for (smaller vs. larger).
Hints
Recall what a straight angle is
What is the measure, in degrees, of a straight angle? Use that to find what the two adjacent angles must add up to.
Set up a variable
Let be the measure of the smaller angle. How can you express the measure of the larger angle in terms of if it is 4 times the smaller?
Write the equation
Write an equation that shows the sum of the two angle expressions equals the measure of a straight angle, and then solve for .
Desmos Guide
Translate to an equation
From the setup, the two angles satisfy , which simplifies to , so .
Use Desmos to compute the value
In Desmos, type 180/5 as an expression. The value that Desmos outputs is the measure of the smaller angle in degrees.
Step-by-step Explanation
Use the fact about a straight angle
A straight angle measures . If two angles are adjacent and form a straight angle, then their measures add up to degrees.
Define a variable for the smaller angle
Let the measure of the smaller angle be degrees. The other angle is 4 times as large, so its measure is degrees.
Write and simplify the equation
Because the two angles form a straight angle, their measures must add to :
Combine like terms:
Solve for the smaller angle
Solve by dividing both sides by 5:
So, the measure of the smaller angle is degrees.