Answer: x = 110 and y = 80
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Step-by-step explanation:
Let z be adjacent to angle y, and angle z is inside the triangle on the right.
Adding up the inside angles of any triangle always gets us to 180 degrees.
We'll use this fact to find z.
z+30+50 = 180
z+80 = 180
z = 180-80
z = 100
Angle y and angle z are supplementary angles. They form a straight line of 180 degrees.
So,
y+z = 180
y+100 = 180
y = 180-100
y = 80
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We can follow the same steps as in the previous section to determine that angle x is 110 degrees.
A shortcut is to use the Remote Interior Angle Theorem.
This theorem says that adding two interior angles will get us the exterior angle that isn't adjacent to either interior angle mentioned.
Notice for instance that angle x is not adjacent to the bottom-left 30 degree angle nor is it adjacent to angle y.
Furthermore, you could use the Remote Interior Angle Theorem to determine the measure of angle y. Note how y = 30+50 = 80. This time the "30" we focus on here is inside the triangle on the right.