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In ΔCDE, \text{m}\angle C = (5x+18)^{\circ}m∠C=(5x+18) ∘ , \text{m}\angle D = (3x+2)^{\circ}m∠D=(3x+2) ∘ , and \text{m}\angle E = (x+16)^{\circ}m∠E=(x+16) ∘ . Find \text{m}\angle D.M∠D.

Respuesta :

Answer:

Angle D = m∠D= 50°

Step-by-step explanation:

In ΔCDE we are given: 3 angles

m∠C=(5x+18) ∘

m∠D=(3x+2) ∘

m∠E=(x+16) ∘ .

The sum of angles in a triangle = 180°

Hence:

m∠C + m∠D + m∠E = 180°

(5x+18)° + (3x+2)° + (x+16)° = 180°

5x + 18 + 3x + 2 + x + 16 = 180°

5x + 3x + x + 18 + 2 + 16 = 180°

9x +36= 180°

Subtract 36 from both sides

9x + 36 - 36 = 180° - 36°

9x = 144°

x = 144°/9

x = 16

From the above question, we are asked to find:angle D (m∠D )

Hence:

m∠D=(3x+2)°

m∠D=( 3 × 16 + 2)°

m∠D=(48 + 2)°

m∠D= 50°

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