Answer to Question #302 in Geometry for Leonard

Question

Can both the adjacent angles be (a) acute angles, (b) obtuse angles, (c) right angles?

Answer 1

The property of adjacent angles: their sum is equal to 1800

(a)Acute angles – the angles which are smaller than a right angle (less than 90°) => their sum will be less then 1800. So both adjacent angles can’t be acute angles.
(b) 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 1800. So both adjacent angles can’t be obtuse angles.
(c) Right angles are both equal to 90°, their sum is equal to 180°. So both adjacent angles can be right angles.