how do you find out the measures of angles

Well we use what we know, that a triangle and a line is equivalent to 180° to find the interior angles of a triangle and possibly use the exterior (s) angles present.

An exterior angle is equivalent to the two most isolated (as in the ones all the way on the other side) interior angles combined.


So this means that m∠Y is equivalent to 138° - 79° which is 59°

Now that we know m∠Y we can find m∠XZY.

How?

Well as I had mentioned earlier a triangle has 180° we can add the two interior angles that we know and subtract it by 180°.

m∠Y and m∠X together is 59° and 79° respectively which is 138°. Now let's subtract it by 180° and get 42°

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m∠XZY = 42°

m∠Y = 59°

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I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey