Will get 1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem b) triangle exterior angles theorem and vertical angles theorem c) triangles angle-sum theorem and angles addition postulate d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m< 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the previous question? (2 points) (2 answers) same-side interior angles theorem vertical angles theorem triangle angle-sum theorem triangle exterior angle theorem alternate exterior angles theorem 4. find the value of x a) x=5 b) x=13 c) x=37 d) x=73

Answers:

1.

Part A. Option a) vertical angles theorem and triangle angle-sum theorem

Part B. Option b) x=80, y=80

2. Option d) 123

3. Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Option c) x=37

Solution:

1. Part A

First, you can find x using the triangle angle-sum theorem: The sum of the interior angles of any triangle must be equal to 180°.

Second, you can apply the vertical angles theorem to find y: the angles opposite by the vertex must be congruent.

Then, the answer is option a) vertical angles theorem and triangle angle-sum theorem.

1. Part B.

First: Triangle angle-sum theorem

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are x°, 30°, and 70°, then:

x°+30°+70°=180°

(x+30+70)°=180°

(x+100)°=180°

x+100=180

Solving for x: Subtracting 100 both sides of the equation:

x+100-100=180-100

x=80

Second: Vertical angles theorem: The angles opposite by the vertex must be congruent:

In the figure, the angles x° and y° are opposite by the vertex, then they must be congruent:

y°=x°

y=x

and x=80, then:

y=80

Option b) x=80, y=80

2. The <1 is an exterior angle of the triangle in the figure, and according with the Triangle Exterior Angle Theorem, an exterior angle of a triangle must be equal to the sum of the interior angles no adjacents to it:

<1=60°+63°

<1=123°

Option d) 123

3.

You can apply the Triangle Angle-Sum Theorem, to find the third interior angle of the triangle. With this angle you can find the exterior <1.

You can apply the Triangle Exterior Angle Theorem to find the exterior <1.

Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Using the Triangle angle-sum theorem:

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are (2x-9)°, x°, and (2x+4)°, then:

(2x-9)°+x°+(2x+4)°=180°

(2x-9+x+2x+4)°=180°

Adding similar terms:

(5x-5)°=180°

5x-5=180

Solving for x: Adding 5 both sides of the equation:

5x-5+5=180+5

Adding:

5x=185

Dividing both sides of the equation by 5:

(5x)/5=185/5

x=37

Option c) x=37

1. Part A

C

Part B

A

2a

4c

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step-by-step explanation:

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