Question

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 ∠u.

A) (x+2) degree
B) (3x+3) degree
C) (7x+10) degree
D) (2x+5) degree

Answer 1

Using the properties of the sum of angles in a triangle and algebraic manipulation, the measure of angle U is calculated to be 17 degrees. The provided options appear to contain an error as none match the calculated measure.

Step-by-step explanation:

The question is asking to find the measure of angle u in triangle TUV, given the algebraic expressions for the measures of angles T, U, and V. Since the sum of the angles in a triangle equals 180 degrees, we can set up an equation to find the value of x, which will then be used to find the measure of angle U.

The sum of angles in triangle TUV can be represented by the equation:

m∠T + m∠U + m∠V = 180 degrees

(7x + 10) + (x + 2) + (3x + 3) = 180

Combining like terms, we get:

11x + 15 = 180

Subtracting 15 from both sides, we have:

11x = 165

Dividing both sides by 11 gives us:

x = 15

Now we can find the measure of angle U by substituting x = 15 into the expression for m∠U:

m∠U = (15 + 2) degrees = 17 degrees

Therefore, the correct answer for the measure of angle U is 17 degrees, which is not one of the options provided, indicating a typo or error in the options.