an angle is 45 degree less than two times of its supplement, then the greater angle is

Let the angle be x.

x = 2(180-x) -45
= 360 -2x -45
= 315 -2x
3x = 315
x = 105 degrees
supplement of x = 75

Let's assume the measure of the angle is x degrees.

According to the given information, the angle is 45 degrees less than two times its supplement.

The supplement of an angle is the angle that, when added to the given angle, forms a straight line (180 degrees).

So, the supplement of the angle is (180 - x) degrees.

Now, we can express the given information as an equation:

x = 2(180 - x) - 45

Simplifying the equation:

x = 360 - 2x - 45

Combining like terms:

x + 2x = 360 - 45

3x = 315

Dividing both sides by 3:

x = 105

Therefore, the greater angle is 105 degrees.

To find the greater angle, let's first understand what is meant by the term "supplement."

The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees. In other words, if an angle is 𝑥, then its supplement is 180 - 𝑥.

Now, let's solve the problem step by step.

Let's assume the angle we are looking for is 𝑎.

According to the given information, 𝑎 is 45 degrees less than two times its supplement.

Mathematically, we can express this as:

𝑎 = 2(180 - 𝑎) - 45

Simplifying the equation:

𝑎 = 360 - 2𝑎 - 45

Combining like terms:

𝑎 + 2𝑎 = 360 - 45

3𝑎 = 315

Dividing both sides by 3:

𝑎 = 315/3

𝑎 = 105

So, the greater angle is 105 degrees.