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.

Answer 1

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.

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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 2

1. 39°
2. x = 38

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.