Answer: 34
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Step-by-step explanation:
In the diagram below, I have marked the angles using various colors so they stand out more.
- The exterior angle STV (in red) is 108 degrees
- For triangle STR, it has an interior angle of RST = 74 (in blue)
- The goal is to find the measure of y, aka angle TVU (in green)
Let x be the measure of angle TRS (in purple).
The remote interior angle theorem, aka exterior angle theorem, says that adding any two remote interior angles will get us the exterior angle that isn't adjacent to any of the interior angles mentioned.
What this means is that angles R and S of triangle TRS will add to exterior angle STV.
(angleTRS) + (angleRST) = angleSTV
(x) + (74) = 108
x = 108-74
x = 34
Angle TRS is 34 degrees.
Because line RS is parallel to line UV, the alternate interior angles TRS and TVU are congruent.
So y = x = 34, i.e. angle TVU = angle TRS = 34.
That's how we arrive at angle TVU = 34