four angles are put together, forming a straight angle. two of the angles are the same size. the other two angles are also the same size but different from the other two. If one of the angles is 40 degrees, what are the measures of the other three? please explain
so you have 2x + 2y = 180
x+y = 90
if x = 40, y = 50
your angles are 40, 40, 50, 50
50
Well, aren't these angles just playing with our minds! Alright, let me put on my math clown shoes and help you figure this out.
So, we have four angles that make up a straight angle, which means they add up to be 180 degrees. Two of the angles are the same size, let's call them x, and the other two angles are also the same size but different from x, let's call them y.
Now, if one of the angles is 40 degrees, we can start by saying:
x + x + y + y = 180
Since we know that x equals 40, we can substitute for it:
40 + 40 + y + y = 180
Simplifying this equation, we get:
80 + 2y = 180
Subtracting 80 from both sides, we have:
2y = 100
Finally, dividing both sides by 2:
y = 50
So, if one angle is 40 degrees, the other two angles would be 40 degrees, and the last angle would be 50 degrees.
Angles sure like to throw us for a loop, don't they? Keep on clowning around with math!
To solve this problem, we need to understand a few concepts related to angles.
1. Straight angle: A straight angle measures exactly 180 degrees. It is formed when two adjacent angles are aligned in a straight line.
2. Equal angles: When two angles have the same measure, we say they are equal.
Based on the given information, we have four angles that form a straight angle. Let's denote the four angles as A, B, C, and D from left to right. We are given that one of the angles, angle A, measures 40 degrees.
To find the measure of the other three angles (B, C, and D), we need to observe the pattern mentioned. Two of the angles are the same size, while the other two angles are also the same size but different from the first two.
Since angle A measures 40 degrees, let's assume angle B is also equal to 40 degrees. This means we have two angles, A and B, measuring 40 degrees each.
Now, we know that the sum of angles in a straight angle is 180 degrees. So, the sum of angles A and B, which are both 40 degrees, is 80 degrees (40 + 40 = 80).
To find the measure of the remaining two angles, C and D, we subtract the sum of angles A and B from the total measure of a straight angle (180 degrees).
180 - 80 = 100
Since angles C and D are equal to each other, their sum is 100 degrees. To find the measure of each angle, we divide this sum by 2:
100 / 2 = 50
Therefore, angles C and D each measure 50 degrees.
In summary, the measures of the four angles are as follows:
Angle A = 40 degrees
Angle B = 40 degrees
Angle C = 50 degrees
Angle D = 50 degrees