∠a and ∠b are vertical angles with m∠a = x and m∠b = 4x – 30. what is m∠a?

∠a and ∠b are vertical angles with m∠a = x and m∠b = 4x - 30. what is m∠a?

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  1. [tex]x = 4x -30[/tex]

    We can solve for x subtracting x on both sides:

    [tex]x-x= 4x-x-30[/tex]

    And then we can add 30 in both sides:

    [tex]30= 3x[/tex]

    And dividing both sides by 3 we got:

    [tex]x = 10[/tex]

    Step-by-step explanation:

    For this case we know the measure of two angles:

    [tex]m <A = x[/tex]

    [tex]m<B = 4x-30[/tex]

    And we know that both angles are vertical and by definition vertical angles are the angles opposite each other when two lines cross.

    For this case since both angles are vertical we have the property that:

    [tex]m<A = m<B[/tex]

    And replacing what we got we have:

    [tex]x = 4x -30[/tex]

    We can solve for x subtracting x on both sides:

    [tex]x-x= 4x-x-30[/tex]

    And then we can add 30 in both sides:

    [tex]30= 3x[/tex]

    And dividing both sides by 3 we got:

    [tex]x = 10[/tex]

  2. we know that

    Vertical Angles are the angles opposite each other when two lines cross. They are always congruent to one another

    in this problem

    ∠A and ​ ∠B ​ are vertical angles

    so

    ∠A=∠B ​

    we have

    ∠A=[tex]x\°[/tex] 

    ∠B=[tex](5x-80)\°[/tex]

    equate angle A and angle B

    [tex]x=5x-80[/tex]

    solve for x

    [tex]5x-x=80[/tex]

    [tex]4x=80[/tex]

    [tex]x=20\°[/tex]

    therefore

    the answer is

    the measure of angle A is [tex]20\°[/tex]

  3. we know that

    Vertical angles are congruent angles opposite each other where two lines cross

    so

    in this problem

    m∠A=m∠B

    so

    substitute the values

    [tex]x=3x-60\\3x-x=60\\2x=60\\x=60/2\\x=30\°[/tex]

    therefore

    the answer is

    The measure of angle A is [tex]30\°[/tex]

  4. m∠A=30°

    Step-by-step explanation:

    we know that

    Vertical Angles are the angles opposite each other when two lines cross.

    Vertical angles always are congruent

    In this problem

    m∠A=m∠B ----> by vertical angles

    we have

    m∠A=x

    m∠B=3x-60

    substitute

    [tex]3x-60=x[/tex]

    Solve for x

    [tex]3x-x=60[/tex]

    [tex]2x=60[/tex]

    [tex]x=30[/tex]

    therefore

    m∠A=30°

  5. m∠A=10°

    Step-by-step explanation:

    we know that

    Vertical angles are the angles opposite each other when two lines cross. The angles are congruent.

    so

    In this problem we have

    m∠A=m∠B

    substitute the given values

    [tex]x=4x-30[/tex]

    Solve for x

    [tex]4x-x=30\\3x=30\\x=10[/tex]

    Find the measure of angle A

    m∠A=x

    substitute the value of x

    m∠A=10°

  6. ∠A and ∠B are vertical angles
    so
    ∠A =∠B 
       x = 4x - 30
    4x - x = 30
    3x = 30
      x = 10

    m<A= x = 10

    answer
    m<A = 10

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