Answer to Question #322 in Geometry for marta s

Question

Can a triangle contain (a) two obtuse angles, (b) one obtuse angle and one right angle, (c) two right angles?

Answer 1

The property of a triangle: the sum of all angles in the triangle is equal to 180°.

(a) obtuse angles – the angles which are larger than a right angle and smaller than a straight angle (between 90° and 180°) => their sum will be more then 180°. So a triangle can not contain two obtuse angles.

(b) obtuse angle – the angle which is larger than a right angle and smaller than a straight angle (between 90° and 180°), the right angle is equal to 90° => their sum will be more then 180°. So a triangle can not contain one obtuse angle and one right angle.

(c) right angles are both equal to 90°, so their sum is equal to 180° => the third angle should be equal to 0. So a triangle can not contain two right angles.