One of two complementary angles has a measure that is five times that of the other. Which equation could be used to find x, the degree measure of the smaller angle?
A) 5x=90
B) x+5x=90
C) 5x=180
D) x=5x=180
I chose A but I wasn't sure if I was correct. Could someone please tell me if I am right or not.
B is the common answer, so I choose B
So, for the bigger angle, the equation is 5x. It can't be A because that would be solving for the larger angle. You can't pick C or D either because the angle is complementary, meaning the two angles equal 90 degrees. So, that leaves you with B: x + 5x = 90 which is the correct answer. Sorry this response was almost 8 years late...I was only 5 when you asked the question.
To solve this problem step-by-step, let's assign variables to the two complementary angles.
Let's say x is the degree measure of the smaller angle.
Since we are given that one angle is five times the other, the measure of the larger angle can be represented as 5x.
Remember that complementary angles add up to 90 degrees.
Using the assigned variables, we can set up the equation for the sum of the two angles:
x + 5x = 90
Simplifying this equation, we get:
6x = 90
To find the value of x, we can divide both sides of the equation by 6:
x = 90/6
x = 15
Therefore, the correct equation to find x, the degree measure of the smaller angle, is:
B) x + 5x = 90
To solve this problem, let's break it down step by step:
1. Let's assume that the smaller angle measures x degrees.
2. According to the problem, the larger angle is five times that of the smaller angle. So, the larger angle measures 5x degrees.
Now, since we know that the sum of complementary angles is 90 degrees, we can set up an equation:
x + 5x = 90
Simplifying the equation, we get:
6x = 90
To solve for x, we divide both sides of the equation by 6:
x = 90/6
Simplifying further, we get:
x = 15
So, the degree measure of the smaller angle is 15 degrees.
Now, let's check which equation matches our solution:
A) 5x = 90
If we substitute x = 15, we get 5(15) = 75 which is not equal to 90. So, this equation is incorrect.
B) x + 5x = 90
If we substitute x = 15, we get 15 + 5(15) = 15 + 75 = 90. So, this equation is correct.
C) 5x = 180
If we substitute x = 15, we get 5(15) = 75 which is not equal to 180. So, this equation is incorrect.
D) x = 5x = 180
This equation is not properly formatted and does not make sense mathematically.
Therefore, the correct equation to find x, the degree measure of the smaller angle, is:
B) x + 5x = 90