In a quadrilateral, the three angles are 61 °, 205 °, and 42 °. What is the fourth angle?

univerkov | February 17, 2021 | education

Let’s apply the property of the sum of the angles of a polygon: the sum of the angles of a convex n-gon is (n-2) * 180, where n is the number of corners of the polygon.
We have n = 4, then the sum of the angles is (n-2) * 180 ° = (4-2) * 180 ° = 2 * 180 ° = 360 °.
We find the sum of the known angles: 61 ° + 205 ° + 42 ° = 308 °.
360 ° -308 ° = 52 ° is the fourth angle.
Answer: 52 °.

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