# Find the degree measure of the angles that are obtained when two straight lines intersect if the sum of 3 is 270 degrees

When two lines intersect, ∠1, ∠2, ∠3 and ∠4 are formed (clockwise).
∠1 = ∠3 = x as vertical; ∠2 = ∠4 = y as vertical.
By condition:
∠1 + ∠2 + ∠3 = 270 °;
x + y + x = 270 °;
2 * x + y = 270 °.
∠1 + ∠2 = 180 °, since these angles are adjacent, then:
x + y = 180 °.
Let’s solve the system of linear equations:
2 * x + y = 270 °;
x + y = 180 °.
In the second equation, we express x:
x = 180 ° – y.
Substitute the resulting expression into the first equation:
2 * (180 ° – y) + y = 270 °;
360 ° – 2 * y + y = 270 °;
– y = 270 ° – 360 °;
– y = – 90 °;
y = 90 °.
Find x:
x = 180 ° – y = 180 ° – 90 ° = 90 °.
Then:
∠1 = ∠3 = x = 90 °, ∠2 = ∠4 = y = 90 °.
Answer: ∠1 = 90 °, ∠2 = 90 °, ∠3 = 90 °, ∠4 = 90 °.

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