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MisterBrainly
5 months ago

Светило науки - 2681 ответа - 0 помощи
Sum of two interiors=exterior

- x²+1+4x+3=2x²+3x-2
- x²+4x+4=2x²+3x-22
- x+6=x²
- x²-x+6=0
- (x-3)(x+2)=0

Take it positive

- x=3

Now

- 2x²+3x-2
- 2(3)²+3(3)-2
- 2(9)+9-2
- 18+7
- 25

Now

<DBC=180-25=155°

Answer:∠DBC = 155°

Step-by-step explanation:Assuming that ABC is a straight line.

Angles on a straight line sum to 180°.

⇒ (2x² + 3x - 2) + ∠DBC = 180°

⇒ ∠DBC = 180° - (2x² + 3x - 2)

The sum of the interior angles of a triangle is 180°:

⇒ (x² + 1) + (4x + 3) + ∠DBC = 180°

⇒ ∠DBC = 180° - (x² + 1) - (4x + 3)

Therefore, we can equate the equations and solve for x:

⇒ ∠DBC = ∠DBC

⇒ 180 - (2x² + 3x - 2) = 180 - (x² + 1) - (4x + 3)

⇒ 180 - 180 = (2x² + 3x - 2) - (x² + 1) - (4x + 3)

⇒ (2x² + 3x - 2) - (x² + 1) - (4x + 3) = 0

⇒ 2x² + 3x - 2 - x² - 1 - 4x - 3 = 0

⇒ x² - x - 6 = 0

⇒ x² + 2x - 3x - 6 = 0

⇒ x(x + 2) - 3(x + 2) = 0

⇒ (x + 2)(x - 3) = 0

Therefore, x = -2, x = 3

As angles are positive, x = 3 only

Substituting found value of x into the angle expressions:

⇒ ∠BDC = x² + 1 = (3)² + 1 = 10°

⇒ ∠DCB = 4x + 3 = 4(3) + 3 = 15°

The sum of the interior angles of a triangle is 180°:

⇒ ∠DBC + ∠BDC + ∠DCB = 180°

⇒ ∠DBC = 180° - ∠BDC - ∠DCB

⇒ ∠DBC = 180° - 10° - 15°

⇒ ∠DBC = 155°