The angles are adjacent and form an angle of 140.the smaller is 28 less than the larger
Let's call the larger angle x.
According to the information given, the smaller angle is 28 less than the larger angle. To express this relationship mathematically, we can write:
Smaller angle = Larger angle - 28
Since the angles are adjacent and form an angle of 140 degrees, we can also write:
Smaller angle + Larger angle = 140
Now, let's substitute the value we found for the smaller angle into the second equation:
(Larger angle - 28) + Larger angle = 140
Simplifying the equation, we have:
2Larger angle - 28 = 140
Adding 28 to both sides of the equation:
2Larger angle = 168
Dividing both sides of the equation by 2:
Larger angle = 168 / 2
Larger angle = 84
Now, let's substitute the value we found for the larger angle into the first equation to find the smaller angle:
Smaller angle = 84 - 28
Smaller angle = 56
Therefore, the larger angle is 84 degrees, and the smaller angle is 56 degrees.
To find the measures of the angles, you can set up an equation based on the given information. Let's represent the smaller angle as "x" and the larger angle as "x + 28" (since the smaller angle is 28 less than the larger angle).
According to the problem, the angles are adjacent, meaning they share a common side and vertex. Adjacent angles add up to form a straight line, which is 180 degrees. In this case, we can set up the equation:
x + (x + 28) = 180
Now, we can solve for "x" by simplifying the equation:
2x + 28 = 180
Subtracting 28 from both sides:
2x = 180 - 28
2x = 152
Dividing by 2:
x = 152 / 2
x = 76
Therefore, the smaller angle is 76 degrees (x) and the larger angle is 76 + 28 = 104 degrees (x + 28).
If x is the larger angle, then
x-28 + x = 140
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