Answer:
The values of x and y are:
x = 38 °
y = 46 °
The angles (2x - 30 °) and y are opposed by the vertex, so they are congruent, that is, they have the same measure. Then:
y = 2x - 30 ° (I)
The angles (3x + 20 °) and y are supplementary, as the sum of it results in a shallow angle, whose measurement is 180 °. Then:
y + 3x + 20 ° = 180 ° (II)
Substituting (I) in (II), we have:
2x - 30 ° + 3x + 20 ° = 180 °
2x + 3x - 30 ° + 20 ° = 180 °
5x - 10 ° = 180 °
5x = 180 ° + 10 °
5x = 190 °
x = 190 °
5
x = 38 °
Now, we calculate the value of y.
y = 2x - 30 °
y = 2.38 ° - 30 °
y = 76 ° - 30 °
y = 46 °
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