Let (2x-12) degrees represent the measure of an acute angle. What are the possible values of x.
Need help lost how to solve
since the angle is acute,
2x - 12 < 90
2x < 102
x < 51
Thanks you so much
To find the possible values of x, we need to consider the given condition that the measure of the angle is acute. An acute angle has a measure between 0 and 90 degrees.
Given: (2x-12) degrees is an acute angle
To satisfy this condition, we can set up the following inequality:
0 < 2x - 12 < 90
Let's solve this inequality step by step:
First, we can add 12 to all parts of the inequality:
0 + 12 < 2x - 12 + 12 < 90 + 12
12 < 2x < 102
Next, divide all parts of the inequality by 2:
12 / 2 < 2x / 2 < 102 / 2
6 < x < 51
Therefore, the possible values of x are between 6 and 51, exclusive of both limits. In interval notation, the solution is (6, 51).