Two angles are supplementary if their sum is 180 degrees the larger angle measures 6 degrees more than twice the measure of the smaller angle if x represents the measure of the smaller angle and these two angles angles are supplementary find the measure of each angle

Question

Two angles are supplementary if their sum is 180 degrees the larger angle measures 6 degrees more than twice the measure of the smaller angle if x represents the measure of the smaller angle and these two angles angles are supplementary find the measure of each angle

Answer 1

Let the smaller angle = x.

x + 2x + 6 = 180

3x = 174

x = 58

Answer 2

The sum of the measures of angle X and angle Y is 90. If the measure of angle X is 30 less than twice the measure of angle Y, what is the measure of angle X?

Answer 3

Let's represent the measure of the smaller angle as x.

According to the problem, the larger angle measures 6 degrees more than twice the measure of the smaller angle. So, the measure of the larger angle is 2x + 6.

Since the two angles are supplementary, their sum is 180 degrees. We can write an equation to represent this:

x + (2x + 6) = 180

To solve this equation, we can combine like terms:

3x + 6 = 180

Next, we can isolate the term with x by subtracting 6 from both sides of the equation:

3x = 180 - 6
3x = 174

Finally, we can solve for x by dividing both sides of the equation by 3:

x = 174 / 3
x ≈ 58

So, the measure of the smaller angle is approximately 58 degrees.

To find the measure of the larger angle, we can substitute x back into the expression 2x + 6:

2(58) + 6
116 + 6
The measure of the larger angle is 122 degrees.

Therefore, the smaller angle measures approximately 58 degrees, and the larger angle measures 122 degrees.

Answer 4

To find the measure of each angle, let's assign variables:

Let x be the measure of the smaller angle.
According to the given information, the larger angle measures 6 degrees more than twice the measure of the smaller angle. Therefore, the larger angle can be represented as 2x + 6.

Since the two angles are supplementary, their sum is 180 degrees. We can set up the following equation:

x + (2x + 6) = 180

Simplifying the equation:
Combine like terms: 3x + 6 = 180
Subtract 6 from both sides: 3x = 174
Divide by 3: x = 58

So, the measure of the smaller angle is 58 degrees.
To find the measure of the larger angle, substitute the value of x back into the expression for the larger angle:

2x + 6 = 2(58) + 6 = 116 + 6 = 122

Therefore, the measure of the larger angle is 122 degrees.