In ΔUVW, \overline{UW} UW is extended through point W to point X, \text{m}\angle UVW = (3x+4)^{\circ}m∠UVW=(3x+4) ∘ , \text{m}\angle VWX = (8x-12)^{\circ}m∠VWX=(8x−12) ∘ , and \text{m}\angle WUV = (x+20)^{\circ}m∠WUV=(x+20) ∘ . What is the value of x?X?

The value of x is 9°

Step-by-step explanation:

The given parameters are;

ΔUVW with side UW extended to X

m∠UVW = (3x + 4)°

m∠VWX = (8x -12)°

m∠WUV = (x + 20)°

We have that m∠UVW + m∠WUV  + m∠VWU = 180° (Sum of the interior angles of a triangle theorem)

∴ m∠VWU = 180° - (m∠UVW + m∠WUV)

Also we have that m∠VWX and m∠VWU are supplementary angles, (The sum of angles on a straight line)

∴  m∠VWX + m∠VWU = 180° (Definition of supplementary angles)

m∠VWU = 180° - m∠VWX

∴ m∠VWX = (m∠UVW + m∠WUV)

Substituting the values, gives;

(8x -12)° = (3x + 4)° + (x + 20)°

8x - 3x - x = 4 + 20 + 12

4x = 36

x = 36/4 = 9

x = 9°.

step-by-step explanation:

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