# One of the base angles of an isosceles triangle is 40 degrees less than the outer base angle.

May 29, 2021 | education

| **One of the base angles of an isosceles triangle is 40 degrees less than the outer base angle. Find the outer corner.**

Let’s denote the vertices of the triangle as a, b, and c. And the angles at the base will be <a = <c, and the angle <b is the angle at the apex. The outer angle is with any of the angles at the base, <a or <c in the sum of 180 degrees, and the angle itself is 40 degrees less. Let’s write it like this:

<c + (<c + 40 °) = 180 °; 2 * <c = 180 ° – 40 ° = 140 °.

Then <c = 140 ° / 2 = 70 °.

Let’s define an external angle with an angle <c.

The outer desired angle is (40 ° + <c) = 70 ° + 40 ° = 110 °.

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