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

August 21, 2021 | education

| 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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