1) A billboard on level ground is supported by a brace, as shown in the accompanying diagram. The measure of angle A is 15 degrees is greater than twice the measure of Angle B. Determine the measure of Angle A and the measure of angle B.

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To solve this problem, we need to use the given information that the measure of angle A is 15 degrees greater than twice the measure of angle B.

Let's assume the measure of angle B is x degrees.
According to the given information, the measure of angle A is 15 degrees greater than twice the measure of angle B. So, the measure of angle A is 2x + 15 degrees.

The sum of the measures of angles A, B, and the right angle at the bottom of the diagram (90 degrees) is equal to 180 degrees because the angles form a triangle.

Therefore, we can write the equation:
A + B + 90 = 180

Substituting the values we have for A and B:
(2x + 15) + x + 90 = 180

Combine like terms:
3x + 105 = 180

Subtract 105 from both sides to isolate 3x:
3x = 75

Divide both sides by 3 to solve for x:
x = 25

Now that we have the value of x, we can find the measure of angle A:
A = 2x + 15
A = 2(25) + 15
A = 50 + 15
A = 65

Therefore, the measure of angle A is 65 degrees and the measure of angle B is 25 degrees.

To solve for the measures of Angle A and Angle B, we can set up an equation based on the given information.

Let x represent the measure of Angle B.

According to the problem, Angle A is 15 degrees greater than twice the measure of Angle B.

So, Angle A = 2x + 15.

The sum of Angle A and Angle B is 180 degrees (since they are supplementary angles).

Therefore, we have the equation:

Angle A + Angle B = 180

Substituting the values we found for Angle A and Angle B, we get:

(2x + 15) + x = 180

Combining like terms:

3x + 15 = 180

Now, we can solve for x.

Subtracting 15 from both sides of the equation:

3x = 180 - 15

3x = 165

Dividing both sides of the equation by 3:

x = 55

Now that we've found x as 55, we can substitute this value back into the equation to find Angle A:

Angle A = 2(55) + 15
= 110 + 15
= 125

Therefore, the measure of Angle A is 125 degrees, and the measure of Angle B is 55 degrees.