In a triangle where the first angle is greater than the second angle by 18° and less than the third angle by 10%, we can set up the following relationships:
1. Let the second angle be x degrees.
2. The first angle is then x + 18 degrees.
3. The third angle is x + 0.10x = 1.10x degrees.
Since the sum of the three angles in a triangle is always 180 degrees, we can write the equation:
x + (x + 18) + 1.10x = 180
Solving this equation will give us the values of x, x + 18, and 1.10x which represent the angles in the triangle.
For the second part of the question where the sum of two angles is 99 degrees and their difference is 10%, we can set up the following relationships:
1. Let one angle be x degrees.
2. The other angle is then 99 - x degrees.
3. The difference between the two angles is 0.10 times their sum, so we have the equation:
0.10(99) = |x - (99 - x)|
Solving this equation will give us the values of x and 99 - x which represent the two angles with the given conditions.
