Obtuse angles measure strictly between 90° and 180°. Since 90° < 127° < 180°, this angle is obtuse. Acute angles fall between 0° and 90°, a right angle is exactly 90°, and a straight angle is exactly 180°. Knowing the boundary values (90° and 180°) precisely is key — an angle of exactly 90° is right, not obtuse.
Question 2 True / False
If you extend the rays of an angle to make them longer, the angle's measure increases.
TTrue
FFalse
Answer: False
An angle's measure depends only on the rotation between the two rays, not on their length. Making the rays longer changes the visual size of the figure but not the angle itself. This is one of the most persistent misconceptions in geometry — students sometimes equate 'bigger-looking' with 'larger angle', but a protractor placed at the vertex reads the same measure regardless of ray length.
Question 3 Short Answer
Ray BD lies in the interior of angle ABC. If m∠ABD = 35° and m∠DBC = 55°, what is m∠ABC and what postulate justifies this?
Think about your answer, then reveal below.
Model answer: m∠ABC = 90°, justified by the Angle Addition Postulate: when a ray lies in the interior of an angle, the two smaller angles it creates sum to the whole angle. So m∠ABC = m∠ABD + m∠DBC = 35° + 55° = 90°.
The Angle Addition Postulate is the angle analogue of the Segment Addition Postulate. It formalizes the intuitive idea that a whole angle equals the sum of its parts. It is the workhorse behind most geometric proofs involving angle relationships and is applied constantly when working with parallel lines, triangles, and polygons.