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
Question
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.
2 Answer

1. User Answers A320Aviation
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=180141
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.
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2.) Because line a is parallel to line b and is intersected by a transversal, t, angles 2x15 and 3x+5 must be sameside exterior angles. According to the sameside exterior angles theorem, these angles are supplementary, meaning that sum up to 180.° So, let’s create an equation and solve for x:
(2x15)+(3x+5)=180
Combine like terms:
2x+3x15+5=180
5x10=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
(7615)+(114+5)=180
61+119=180
180=180
So, x=38 is correct for part 2. 
2. User Answers sqdancefan
Answer:
 39°
 x = 38
Stepbystep 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
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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.