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Angle DEF and GEH have the following meaure:

m∠DEF = (x − 18)°, m∠GEH = (3x 4)°

Part A: If angle DEF and angle GEH are complementary angle, find the value of x. Show every tep of your work. (4 point)

Part B: Ue the value of x from Part A to find the meaure of angle DEF and GEH. Show every tep of your work. (4 point)

Part C: Could the angle alo be vertical angle? Explain. (4 point)

Respuesta :

akposevictor

A. Applying the definition of complementary angles, the value of x = 26

B. m∠DEF = 8°; m∠GEH = 82°

C. ∠DEF and ∠GEH are not congruent, therefore, they are not vertical angles.

What are Complementary and Vertical Angles?

If we add two angles together and it is equal to 90 degrees, it means both angles are complementary angles.

On the other hand, if two angles are referred to as vertical angles, based on the vertical angles theorem, both angles will be equal to each other.

The angles that are vertical angles and are also complementary are angles 45°. This means for two angles to be complementary and also vertical angles, they must each equal 45 degrees.

Part A:

Angles DEF and GEH are complementary angles, therefore:

m∠DEF = m∠GEH

Substitute

(x − 18)° + (3x + 4)° = 90

x − 18 + 3x + 4 = 90

4x - 14 = 90

Combine like terms

4x - 14 + 14 = 90 + 14

4x = 104

x = 26

Part B:

m∠DEF = (x − 18)° = 26 - 18 = 8°

m∠GEH = (3x + 4)° = 3(26) + 4 = 82°

Part C:

Both angles cannot be vertical angles because they are not congruent to each other.

Learn more about complementary and vertical angles on:

https://brainly.com/question/22256947

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