One of the outer corners of the triangle is 90 degrees. Angles not adjacent to a given external angle are 1: 2.

One of the outer corners of the triangle is 90 degrees. Angles not adjacent to a given external angle are 1: 2. Find the largest one.

1. A, B, C – the vertices of the triangle. The external apex angle is A = 90 °.

2.∠А = 180 ° – 90 ° = 90 °.

3. ∠В: ∠С = 1: 2. Therefore, ∠С = 2∠В.

4. The total value of all internal angles of the triangle, according to its properties, is 180 °:

∠В + ∠С + ∠А = 180 °. We substitute in this expression 2∠В instead of ∠С:

∠В + 2∠В + 90 ° = 180 °.

3∠B = 90 °.

∠В = 30 °.

∠С = 2∠В = 2 x 30 ° = 60 °.

Answer: ∠С = 60 ° – a larger acute angle.