Mathematics

Question

I'm not good with this type of thing in math so I need help.
1 .▲PQR has angle measures of 108 degrees, 33 degrees, and x degrees.

Describe how to find the missing angle measure, then determine its measurement. ( I also have to show my work.

2. Line a || Line b.

Use the diagram to write an equation and solve for x.
I'm not good with this type of thing in math so I need help. 1 .▲PQR has angle measures of 108 degrees, 33 degrees, and x degrees. Describe how to find the miss
I'm not good with this type of thing in math so I need help. 1 .▲PQR has angle measures of 108 degrees, 33 degrees, and x degrees. Describe how to find the miss

2 Answer

  • 1.) The Triangle Sum Theorem states that all three interior angles in a triangle sum up to 180.° Therefore, in triangle PQR, 108°+33°+x°=180.° Notice that we have an unknown angle measure, x, which we know is one of the three interior angles in triangle PQR. Let’s solve for x:

    108+33+x=180

    Combine like terms:

    141+x=180

    Subtract 141 from both sides:

    x=180-141

    x=39

    So, x°=39°

    We can check this by plugging it back into the triangle sum equation:

    108+33+(39)=180

    180=180

    So, x=39 is correct.

    —————————————————————

    2.) Because line a is parallel to line b and is intersected by a transversal, t, angles 2x-15 and 3x+5 must be same-side exterior angles. According to the same-side exterior angles theorem, these angles are supplementary, meaning that sum up to 180.° So, let’s create an equation and solve for x:

    (2x-15)+(3x+5)=180

    Combine like terms:

    2x+3x-15+5=180

    5x-10=180

    Add 10 to both sides:

    5x=180+10

    5x=190

    Divide both sides by 5:

    x=190/5

    x=38

    Now, let’s check x in the equation to determine if it is true:

    [2(38)-15]+[3(38)+5]=180

    (76-15)+(114+5)=180

    61+119=180

    180=180

    So, x=38 is correct for part 2.

  • Answer:

    1. 39°
    2. x = 38

    Step-by-step explanation:

    You want the measure of the third angle in a triangle in which two of the angles are 108° and 33°. You also want the measure of x where consecutive exterior angles at a transversal are (2x -15) and (3x +5).

    1. Angle

    The sum of angles in a triangle is 180°, so the measure of the third can be found by subtracting the other two from 180°:

      x = 180° -108° -33° = 39°

    The missing angle measure is 39°.

    2. Variable

    The two marked angles are "consecutive exterior angles" so have a sum of 180°. This can be used to write an equation.

      (2x -15) +(3x +5) = 180

      5x -10 = 180 . . . . . . . . . . . simplify

      x -2 = 36 . . . . . . . . . . . divide by 5

      x = 38 . . . . . . . . . . . add 2

    __

    Additional comment

    The two angles are 2(38)-15 = 61°, and 3(38)+5 = 119°. They total 180°.

    There are a number of relationships involving angles in various geometries. It is helpful to remember them, or at least keep a handy list.

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