In ΔTUV, m, angle, T, equals, left bracket, 7, x, plus, 10, right bracket, degreesm∠T=(7x+10)∘, m, angle, U, equals, left bracket, x, plus, 2, right bracket, degreesm∠U=(x+2)∘, and m, angle, V, equals, left bracket, 3, x, plus, 3, right bracket, degreesm∠V=(3x+3)∘. Find m, angle, U, .m∠U
We know that in a triangle, the sum of the interior angles is 180 degrees.
So,
m∠T + m∠U + m∠V = 180.
Substituting the given values,
(7x+10) + (x+2) + (3x+3) = 180.
11x + 15 = 180.
Simplifying the equation,
11x = 165,
x = 15.
Now we can substitute the value of x back into the equation for m∠U,
m∠U = (x+2) = 15 + 2 = 17.
Therefore, m∠U is 17 degrees.
To find the measure of angle U (m∠U), you need to substitute the given values into the equation m∠U = (x + 2)°.
From the given information:
m∠T = (7x + 10)°
m∠V = (3x + 3)°
We can set up an equation using the angles of a triangle:
m∠T + m∠U + m∠V = 180°
Substituting the given values:
(7x + 10)° + m∠U + (3x + 3)° = 180°
Combine like terms:
10x + 13 + m∠U = 180°
To isolate m∠U, subtract 13 from both sides of the equation:
10x + m∠U = 180° - 13°
10x + m∠U = 167°
Therefore, the measure of angle U (m∠U) is 167°.
To find m∠U, we need to use the given information about the angles in triangle TUV.
m∠U = (x + 2)°
However, we still need a value for x in order to find m∠U. To determine the value of x, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
m∠T + m∠U + m∠V = 180°
Substituting the given angle measurements:
(7x + 10)° + (x + 2)° + (3x + 3)° = 180°
Combine like terms:
7x + 10 + x + 2 + 3x + 3 = 180
Simplify:
11x + 15 = 180
Now, isolate x by subtracting 15 from both sides:
11x = 165
Divide both sides by 11:
x = 15
Now that we have found the value of x as 15, we can substitute it into the expression for m∠U:
m∠U = (15 + 2)°
m∠U = 17°
Therefore, m∠U is 17 degrees.