Question

question
in \\( \triangle tuv \\), \\( \overline{tv} \\) is extended through point \\( v \\) to point \\( w \\), \\( m\angle tuv = (2x - 7)\degree \\), \\( m\angle uvw = (10x - 14)\degree \\), and \\( m\angle vtu = (3x + 18)\degree \\). find \\( m\angle vtu \\).
answer
attempt 1 out of 2
\\( m\angle vtu = \square \degree \\)
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Explanation:

Step1: Recall Exterior Angle Theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In $\triangle TUV$, $\angle UVW$ is an exterior angle, so $m\angle UVW=m\angle TUV + m\angle VTU$.

Substitute the given angle measures: $(10x - 14)=(2x - 7)+(3x + 18)$

Step2: Simplify the equation

First, simplify the right - hand side: $(2x - 7)+(3x + 18)=2x+3x-7 + 18=5x + 11$

So our equation becomes $10x-14 = 5x+11$

Subtract $5x$ from both sides: $10x-5x-14=5x - 5x+11$ which gives $5x-14 = 11$

Add 14 to both sides: $5x-14 + 14=11 + 14$ which gives $5x=25$

Divide both sides by 5: $x=\frac{25}{5}=5$

Step3: Find $m\angle VTU$

We know that $m\angle VTU=(3x + 18)^{\circ}$. Substitute $x = 5$ into the expression:

$m\angle VTU=3\times5+18=15 + 18=33$

Answer:

$33$