# Can the angle between the bisectors of two angles of a triangle be 90 degrees?

September 29, 2021 | education

| Let in an arbitrary triangle ABC, two angles <A and <B are given. After the bisectors of these angles were drawn, a new triangle was formed with angles <A / 2 and <B / 2. The angle between the bisectors will be equal to: 180 ° – (<A / 2 + <B / 2), and if this angle were equal to 90 °, then 180 ° – (<A / 2 + <B / 2) = 90 °, or (<A / 2 + <B / 2) = 90 °.

This expression is equivalent to the fact that (<A + <B) = 90 ° * 2 = 180 °, but this cannot be, since two angles in a triangle cannot be equal to 180 °, but only three whole angles will add up to 180 °.

Answer: it cannot.

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