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Please help will get brainiest!!

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

Please help will get brainiest 1 Part A Which theorems or postulates allow you to find the value of y a vertical angles theorem and triangle anglesum theorem b class=
Please help will get brainiest 1 Part A Which theorems or postulates allow you to find the value of y a vertical angles theorem and triangle anglesum theorem b class=
Please help will get brainiest 1 Part A Which theorems or postulates allow you to find the value of y a vertical angles theorem and triangle anglesum theorem b class=

Respuesta :

allisonmw8888

1. Part A

C

Part B

A

2a

4c

srry all i can do

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

Answer: 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°

Answer: 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.

Answer: 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

Answer: Option c) x=37

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