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 angle of the four angles is 40 degrees, what are the measures of the other three angles
40 + 40 + 2x = 180
To find the measures of the other three angles, we need to understand the concept of a straight angle. A straight angle is formed when two angles add up to 180 degrees.
In this case, the given information tells us that the four angles form a straight angle. Let's represent the angles as A, B, C, and D.
We know that A + B + C + D = 180 degrees.
From the given information, we also know that two angles are the same size, and the other two angles are also the same size but different from the first two angles.
Let's assume that A and B are the two angles that are the same, and C and D are the other two angles that are the same but different from A and B.
Given that one angle (let's assume it is A) is 40 degrees, we can now solve for the remaining three angles.
Since A + B + C + D = 180 degrees, we have:
40 + B + C + D = 180
Now, we also know that A and B are the same, so B = A = 40 degrees.
Replacing B with 40 in the equation above, we get:
40 + 40 + C + D = 180
Simplifying further, we have:
80 + C + D = 180
Subtracting 80 from both sides, we get:
C + D = 100
Since C and D are the same, their individual measures would be (100 divided by 2):
C = D = 50 degrees.
So, the measures of the other three angles are:
A = B = 40 degrees
C = D = 50 degrees.