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In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98°...Asked by HELP!!!
In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98° , what is the value of x ?(1 point)
Responses
7272
18
18
1414
98
Responses
7272
18
18
1414
98
Answers
Answered by
GPT 3.5
Since ∠1 and ∠3 are a vertical pair, they are congruent angles and have equal measures.
Therefore, 4x + 26 = 98.
Subtracting 26 from both sides of the equation, we get:
4x = 98 - 26.
Simplifying the right side, we have:
4x = 72.
To solve for x, divide both sides of the equation by 4:
x = 72/4.
Simplifying the right side, we get:
x = 18.
Therefore, the value of x is 18.
Therefore, 4x + 26 = 98.
Subtracting 26 from both sides of the equation, we get:
4x = 98 - 26.
Simplifying the right side, we have:
4x = 72.
To solve for x, divide both sides of the equation by 4:
x = 72/4.
Simplifying the right side, we get:
x = 18.
Therefore, the value of x is 18.
Answered by
GPT 3.5
Yes, I am sure. The value of x is 18.
Answered by
GPT 3.5
Since vertical angles are congruent, ∠2 and ∠4 must have equal measures.
Therefore, we can set up the equation:
5x + 23 = 3x + 35.
Subtracting 3x from both sides of the equation, we get:
2x + 23 = 35.
Then, subtracting 23 from both sides, we have:
2x = 12.
Dividing both sides by 2, we get:
x = 6.
Now, we can find the measure of ∠2 and ∠4 by substituting the value of x:
∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.
∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.
Therefore, the measure of each angle is 53 degrees.
Therefore, we can set up the equation:
5x + 23 = 3x + 35.
Subtracting 3x from both sides of the equation, we get:
2x + 23 = 35.
Then, subtracting 23 from both sides, we have:
2x = 12.
Dividing both sides by 2, we get:
x = 6.
Now, we can find the measure of ∠2 and ∠4 by substituting the value of x:
∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.
∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.
Therefore, the measure of each angle is 53 degrees.
Answered by
GPT 3.5
I apologize for the incorrect response.
Let's find the correct measures of ∠2 and ∠4.
From the given information, we have:
m∠2 = (5x + 23)°
m∠4 = (3x + 35)°
Since ∠2 and ∠4 are vertical angles, they must have equal measures.
Therefore, we can set up the equation:
5x + 23 = 3x + 35.
Subtracting 3x from both sides, we get:
2x + 23 = 35.
Subtracting 23 from both sides, we have:
2x = 12.
Dividing both sides by 2, we get:
x = 6.
Now, let's substitute the value of x back into the expressions for ∠2 and ∠4:
m∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.
m∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.
Therefore, the measure of each angle is 53 degrees. I apologize again for the earlier confusion. I am sure that the correct measure for each angle is 53 degrees.
Let's find the correct measures of ∠2 and ∠4.
From the given information, we have:
m∠2 = (5x + 23)°
m∠4 = (3x + 35)°
Since ∠2 and ∠4 are vertical angles, they must have equal measures.
Therefore, we can set up the equation:
5x + 23 = 3x + 35.
Subtracting 3x from both sides, we get:
2x + 23 = 35.
Subtracting 23 from both sides, we have:
2x = 12.
Dividing both sides by 2, we get:
x = 6.
Now, let's substitute the value of x back into the expressions for ∠2 and ∠4:
m∠2 = 5(6) + 23 = 30 + 23 = 53 degrees.
m∠4 = 3(6) + 35 = 18 + 35 = 53 degrees.
Therefore, the measure of each angle is 53 degrees. I apologize again for the earlier confusion. I am sure that the correct measure for each angle is 53 degrees.
Answered by
GPT 3.5
You're welcome! If you have any more questions, feel free to ask.
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