In ΔUVW, start overline, U, W, end overlineUW is extended through point W to point X, m, angle, W, U, V, equals, left bracket, 2, x, plus, 15, right bracket, degreesm∠WUV=(2x+15)∘, m, angle, U, V, W, equals, left bracket, 2, x, plus, 15, right bracket, degreesm∠UVW=(2x+15)∘, and m, angle, V, W, X, equals, left bracket, 8, x, minus, 14, right bracket, degreesm∠VWX=(8x−14)∘. Find m, angle, W, U, V, .m∠WUV..
Since we know that the sum of the angles in a triangle is 180 degrees, we can write the equation:
m∠WUV + m∠UVW + m∠VWX = 180
Substituting the given angle measures into the equation, we have:
(2x + 15) + (2x + 15) + (8x - 14) = 180
Combine like terms:
12x + 16 = 180
Subtract 16 from both sides:
12x = 164
Divide both sides by 12:
x = 13.67
Now substitute x back into the expression for m∠WUV:
m∠WUV = 2x + 15 = 2(13.67) + 15 = 42.34
Therefore, m∠WUV = 42.34 degrees.
To find the measure of angle WUV, we need to equate it to the given expression 2x + 15 degrees:
m∠WUV = 2x + 15 degrees
To find the measure of angle WUV (m∠WUV), we have the given information:
m∠WUV = (2x + 15)°
Now, we need to use the fact that the sum of the angles in a triangle is 180°. In triangle UVW, the sum of the measures of angles WUV (m∠WUV), UVW (m∠UVW), and VWX (m∠VWX) must add up to 180°.
Therefore, we can set up the equation:
m∠WUV + m∠UVW + m∠VWX = 180°
Substituting the given expressions for the angle measures:
(2x + 15)° + (2x + 15)° + (8x - 14)° = 180°
Simplifying the equation:
2x + 15 + 2x + 15 + 8x - 14 = 180
12x + 16 = 180
To solve for x, we isolate the x-term by subtracting 16 from both sides:
12x = 164
Dividing both sides by 12:
x = 164/12
x = 13.67
Now, we can substitute the value of x back into the expression for m∠WUV:
m∠WUV = (2x + 15)°
m∠WUV = 2(13.67) + 15
m∠WUV = 27.34 + 15
m∠WUV = 42.34°
Therefore, the measure of angle WUV (m∠WUV) is 42.34 degrees.