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oeerivona
Answer:
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°.
This can help you to understand it
Remember for this type of question.I'm guessing you make the equation equal to 0. Then square both sides the (X ^2-16) and 0. Then the square root goes away. Then you factor it according to the difference of squares method. By taking the square root of x^2 and 16. So ultimately it turns into 2 binomials according to the difference of squares method. The simplified answer would be (X-4)(X+4)=0. To solve for x in each case, take each respective equation separately and make it equal to 0. Solve for x.
