Answer:
52x5x2 is your answer
Step-by-step explanation:
<em>Question:</em>
The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
—————
<em>Solution:</em>
Call those two angles x and y, where x is the larger one.
If they are complementary, then their sum equals 90°:
x + y = 90° (i)
Also, the ratio between x and y is 3 : 2, so
x 3
—— = ——
y 2
Product of the extremes = product of the means:
2x = 3y
2x – 3y = 0 (ii)
Now, just solve this system of equations:
x + y = 90° (i)
2x – 3y = 0 (ii)
Solve it with elimination. Since you want to know the value of the larger angle, which is x, then eliminate the variable y by doing the following:
Multiply the equation (i) by 3,
3x + 3y = 270° (iii)
2x – 3y = 0 (ii)
then add both equations, so you cancel out the variable y:
3x + 2x + 3y – 3y = 270° + 0
3x + 2x = 270°
5x = 270°
270°
x = ———
5
x = 54° <——— this is the measure of the larger angle.
I hope this helps. =)
Tags: <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em>
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The value of x from the given diagram is 17
<h2>Vertically opposite angles</h2>
From the given diagram, m<2 and m<3 are vertically opposite since they form angles from the intersection of lines at the point X
Given that;
- m<2 = 4x + 2
- m<3 = 5x - 15
Equate both expressions to have:
m<2 = m<3
4x + 2 = 5x - 15
4x - 5x = -15 - 2
-x = -17
x = 17
Hence the value of x from the given diagram is 17.
Learn more on vertical angles here; brainly.com/question/1673457
