Answer:
[tex]\angle 1=39\textdegree[/tex]
Step-by-step explanation:
Remember that the sum of the interior angles of a triangle always equal 180. Therefore:
[tex]\angle 1+\angle Y+102=180[/tex]
Let's subtract 102 from both sides. This yields:
[tex]\angle 1+\angle Y=78[/tex]
Now, notice the that both ∠1 and ∠Y have exactly one arc mark.
Arc-marks denote congruence. Therefore, ∠1 and ∠Y are congruent to each other. In other words:
[tex]\angle 1=\angle Y[/tex]
So, we can substitute ∠Y for ∠1 for our equation. This yields:
[tex]\angle 1+\angle 1=78[/tex]
Combine like terms:
[tex]2\angle 1=78[/tex]
Divide both sides by 2. So, the measure of our angle is:
[tex]\angle 1=39\textdegree[/tex]
And we're done!
