Question

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? (1 point) Responses 20° 20° 35° 35° 50° 50° 65°

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's say the measure of angle Y is represented by y.

Since the sum of the measures of angle X and angle Y is 90, we can write the equation: X + Y = 90.
We are also told that the measure of angle X is 30 less than twice the measure of angle Y. In equation form, this is: X = 2Y - 30.
Substituting the second equation into the first equation, we get: (2Y - 30) + Y = 90.
Combining like terms, we get: 3Y - 30 = 90.
Adding 30 to both sides, we get: 3Y = 120.
Dividing both sides by 3, we get: Y = 40.
Therefore, the measure of angle X is 2(40) - 30 = 80 - 30 = 50 degrees.
So the answer is 50°.

Answer 2

[AI-generated answer — Step-by-Step Bot]

Let's let the measure of angle Y be represented by variable y.

According to the information given, the sum of the measures of angle X and angle Y is 90 degrees.

So, we can write the equation: X + Y = 90.

The problem also states that the measure of angle X is 30 less than twice the measure of angle Y.

This can be written as: X = 2Y - 30.

To find the measure of angle X, substitute the value of X from the second equation into the first equation:

2Y - 30 + Y = 90

Combining like terms, we get:

3Y - 30 = 90

Add 30 to both sides:

3Y = 120

Divide both sides by 3:

Y = 40

Now we can substitute this value back into the second equation to find the measure of angle X:

X = 2(40) - 30
X = 80 - 30
X = 50.

Therefore, the measure of angle X is 50°.

Answer 3

[AI-generated answer — Explain Bot]

To find the measure of angle X, we can start by defining our variables. Let's say that the measure of angle Y is represented by the variable 'y'.

According to the information given, the sum of the measures of angle X and angle Y is 90. Therefore, we can write the equation as:

X + Y = 90

We are also told that the measure of angle X is 30 less than twice the measure of angle Y. Using this information, we can write the equation as:

X = 2Y - 30

Now we have a system of two equations:

Equation 1: X + Y = 90
Equation 2: X = 2Y - 30

To solve this system of equations, we can substitute the value of X from Equation 2 into Equation 1:

2Y - 30 + Y = 90

Combine like terms:

3Y - 30 = 90

Add 30 to both sides:

3Y = 120

Divide both sides by 3:

Y = 40

Now that we have found the value of Y (40), we can substitute it back into Equation 2 to find the value of X:

X = 2(40) - 30
X = 80 - 30
X = 50

Therefore, the measure of angle X is 50°.